Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #10227 |
466 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 99 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)(54,56,58,55)(57,59,61,60)(62,65)(63,70)(64,74)(66,81)(67,80)(68,79)(69,83)(71,88)(72,77)(73,87)(75,91)(76,90)(78,82)(84,93)(85,92)(86,89);(54,55,58,56)(57,60,61,59)(62,64)(63,69)(65,78)(66,75)(67,82)(68,76)(70,86)(71,84)(72,89)(73,85)(74,81)(77,92)(79,91)(80,90)(83,88)(87,93);(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)(55,59)(56,60)(57,61)(62,63,68,73)(64,69,76,85)(65,77,79,88)(66,72,67,71)(70,81,87,80)(74,86,90,93)(75,89,82,84)(78,83,91,92)Polycyclic presentation:
2^8,53|a^2=gh,b^2=g,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fgh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fgh,d^c=dh,e^c=eh,f^c=fgh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 71861);