Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1363 ⋊ C2 |
| Sylow | C53 ⋊ #11978 |
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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)(54,56,58,57)(55,59,60,61)(63,69)(68,83)(70,71)(72,85)(73,91)(84,90)(86,88)(87,89);(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)(56,59)(57,61)(58,60)(62,64)(63,68)(65,78)(66,76)(67,82)(69,83)(70,86)(71,88)(72,90)(73,87)(74,81)(75,92)(77,79)(80,93)(84,85)(89,91);(55,59)(56,57)(60,61)(62,63,65,71,79,85,92,87,66,69,80,70,67,72,81,89)(64,73,75,90,82,88,78,83,76,91,74,84,77,86,93,68)Polycyclic presentation:
2^8,53|a^2=e,c^2=fh,d^2=gh,e^2=fg,g^2=h,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^b=i^52,i^c=i^52806 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81029);