((C2 x C2 x C2 x C2) : C2) x D22
r0 := (1,2)(3,5)(4,7)(6,10)(8,13)(9,12)(11,14)(15,17)(16,18)(19,21)(20,23)(22,25)(24,27)(26,29)(28,30)(31,33)(32,34)(35,37)(36,39)(38,41)(40,43)(42,45)(44,46)(47,49)(48,50)(51,53)(52,55)(54,57)(56,59)(58,61)(60,62)(63,65)(64,66)(67,69)(68,71)(70,73)(72,75)(74,77)(76,78)(79,81)(80,82)(83,85)(84,87)(86,88);
r1 := (1,3)(2,4)(5,9)(6,11)(7,12)(8,14)(10,15)(13,17)(16,20)(18,22)(19,23)(21,25)(24,28)(26,30)(27,31)(29,33)(32,36)(34,38)(35,39)(37,41)(40,44)(42,46)(43,47)(45,49)(48,52)(50,54)(51,55)(53,57)(56,60)(58,62)(59,63)(61,65)(64,68)(66,70)(67,71)(69,73)(72,76)(74,78)(75,79)(77,81)(80,84)(82,86)(83,87)(85,88);
r2 := (3,6)(4,8)(5,10)(7,13)(11,16)(14,18)(15,19)(17,21)(20,24)(22,26)(23,27)(25,29)(28,32)(30,34)(31,35)(33,37)(36,40)(38,42)(39,43)(41,45)(44,48)(46,50)(47,51)(49,53)(52,56)(54,58)(55,59)(57,61)(60,64)(62,66)(63,67)(65,69)(68,72)(70,74)(71,75)(73,77)(76,80)(78,82)(79,83)(81,85);
r3 := (3,4)(5,7)(6,8)(10,13)(20,22)(23,25)(24,26)(27,29)(36,38)(39,41)(40,42)(43,45)(52,54)(55,57)(56,58)(59,61)(68,70)(71,73)(72,74)(75,77)(84,86)(87,88);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r2^2, r3^2, r0^2, r1^2, (r3*r2)^2, (r0*r3)^2, (r0*r2)^2, (r3*r1)^4, (r2*r1*r3*r1)^2, (r1*r0*r1*r2)^2, (r0*r1)^4, (r1*r3*r1*r0)^2, (r1*r2)^22 ];;
type 0: 4 elements
type 1: 88 elements
type 2: 22 elements
type 3: 4 elements