Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1350 ⋊ C2 |
| Sylow | C53 ⋊ #11893 |
400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(56,61)(58,60)(62,65,66,83,68,85,67,84)(63,70,73,90,74,71,72,81)(64,76,78,82,80,77,79,93)(69,75,87,89,88,92,86,91);(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)(55,58)(57,61)(59,60)(62,64)(63,69)(65,82)(66,79)(67,78)(68,80)(70,89)(71,91)(72,87)(73,86)(74,88)(75,90)(76,83)(77,84)(81,92)(85,93);(54,55)(56,60,61,58)(57,59)(62,63,66,72,68,74,67,73)(64,75,78,91,80,92,79,89)(65,81,83,71,85,90,84,70)(69,82,86,77,88,93,87,76)Polycyclic presentation:
2^8,53|a^2=e,c^2=gh,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,g^a=gh,c^b=cf,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^52,i^c=i^52806 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80669);