Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7277 |
222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 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)(54,55,56,59,57,58,60,61)(62,64,67,78,68,79,84,76,69,80,83,92,66,77,65,82)(63,70,73,87,72,86,71,89,74,88,81,93,85,91,90,75);(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)(56,60)(62,63,66,72,69,74,68,85)(64,75,77,87,80,89,79,93)(65,81,83,90,84,73,67,71)(70,78,86,82,88,92,91,76)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fh,d^2=h,e^2=fgh,f^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fh,i^a=i^52,c^b=cg,i^b=i^521514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56764);