Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #13706 |
164 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 65 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) = 13568 |
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)(62,64,65,73)(63,69,68,82)(66,78,75,91)(67,81,76,92)(70,86,80,93)(71,88,79,74)(72,89,90,77)(83,87,84,85);(54,56,57,61)(55,58,59,60)(62,63,65,68)(64,69,73,82)(66,70,75,80)(67,71,76,79)(72,84,90,83)(74,81,88,92)(77,87,89,85)(78,86,91,93);(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)(54,55,57,59)(56,60,61,58)(63,68)(64,72)(66,77)(67,79)(69,83)(70,85)(71,76)(73,90)(74,86)(75,89)(78,81)(80,87)(82,84)(88,93)(91,92)Polycyclic presentation:
2^8,53|a^2=dh,b^2=d,c^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^52,e^c=ef,f^c=fg,g^c=gh,i^c=i^522129 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90466);