Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1338 ⋊ C2 |
| Sylow | C53 ⋊ #11620 |
318 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,56,57,61)(55,58,60,59)(62,65,67,68)(63,70,71,77)(64,74,76,78)(66,79,81,82)(69,83,73,85)(72,86,87,90)(75,89,80,91)(84,92,88,93);(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)(56,58)(57,60)(59,61)(62,64)(63,69)(65,78)(66,80)(67,76)(68,74)(70,85)(71,73)(72,88)(75,81)(77,83)(79,89)(82,91)(84,87)(86,92)(90,93);(54,55,56,58,57,60,61,59)(62,63,66,72,68,70,82,86,67,71,81,87,65,77,79,90)(64,73,75,88,74,83,89,92,76,69,80,84,78,85,91,93)Polycyclic presentation:
2^8,53|a^2=e,c^2=f,d^2=fh,e^2=g,g^2=h,b^a=bd,c^a=ch,d^a=df,c^b=ch,d^b=dfh,e^b=eh,i^b=i^52,i^c=i^521052 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79434);