Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#1998 ⋊ C2 |
| Sylow | C53 ⋊ #33062 |
764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(62,66)(63,71)(64,76)(65,78)(67,81)(68,83)(69,85)(70,87)(72,88)(73,89)(74,90)(75,82)(77,92)(79,91)(80,84)(86,93);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(55,59)(58,61)(62,65,67,77,68,79,75,64)(63,70,72,69,73,74,84,86)(66,78,81,92,83,91,82,76)(71,87,88,85,89,90,80,93);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,56,57,60)(55,58,59,61)(62,64,75,79,68,77,67,65)(63,69,84,70,73,86,72,74)(66,76,82,91,83,92,81,78)(71,85,80,87,89,93,88,90);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,58)(57,59)(60,61)(62,63)(64,74)(65,69)(66,80)(67,84)(68,73)(70,77)(71,82)(72,75)(76,85)(78,87)(79,86)(81,89)(83,88)(90,91)(92,93)Polycyclic presentation:
2^8,53|b^2=fh,c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,f^a=fh,g^a=gh,i^a=i^52,i^b=i^52,i^c=i^52,g^d=gh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 319877);