Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1370 ⋊ C2 |
| Sylow | C53 ⋊ #12429 |
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 6784 |
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)(63,69,68,83)(66,79,76,93)(67,82,77,75)(70,86,84,92)(71,87,81,85)(72,89,88,78)(74,91,90,80);(54,55,59,61,57,60,56,58)(63,68)(69,83)(70,84)(71,81)(72,88)(78,89)(85,87)(86,92);(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)(56,59)(60,61)(62,63)(64,72)(65,68)(66,78)(67,81)(69,74)(70,80)(71,77)(73,88)(75,92)(76,89)(79,87)(82,86)(83,90)(84,91)(85,93)Polycyclic presentation:
2^8,53|b^2=dfh,c^2=h,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^52,e^c=eg,g^c=gh,i^c=i^521499 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83768);