Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1742 ⋊ C2 |
| Sylow | C53 ⋊ #22482 |
1132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 77 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)(55,58)(59,61)(64,71)(67,70)(72,74)(75,77);(54,56,57,60)(55,59,58,61)(63,68)(66,73)(67,70)(72,74);(54,55)(56,59)(57,58)(60,61)(62,64,65,71)(63,67,68,70)(66,72,73,74)(69,75,76,77);(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)(55,58)(59,61)(62,63,66,69,65,68,73,76)(64,70,72,77,71,67,74,75)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=eh,g^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^52,d^b=de,g^c=gh,i^d=i^521199 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 185756);