Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #13542 |
252 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 89 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)(55,59)(58,61)(62,64,65,75,66,76,78,77)(63,69,70,85,71,73,68,82)(67,81,79,74,80,91,93,92)(72,84,87,86,88,89,83,90);(54,56,57,60)(55,58,59,61)(63,68)(64,74,76,92)(65,78)(67,79)(69,84,73,89)(70,71)(75,81,77,91)(80,93)(82,86,85,90)(83,87);(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)(62,63,65,70,66,71,78,68)(64,73,75,82,76,69,77,85)(67,72,79,87,80,88,93,83)(74,90,91,84,92,86,81,89)Polycyclic presentation:
2^8,53|a^2=d,b^2=deg,c^2=d,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^52,c^b=cf,d^b=dh,f^b=fg,g^b=gh,f^c=fg,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89716);