Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9979 |
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,57)(55,60)(56,62)(58,64)(59,65)(61,68)(63,69)(66,67)(70,73,76,90)(71,78,80,97)(72,82,85,100)(74,88,75,89)(77,92,94,99)(79,96,91,86)(81,98,93,95)(83,87,84,101);(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)(54,56,58,63)(55,59,61,66)(57,62,64,69)(60,67,68,65)(70,72)(71,77)(73,87)(74,84)(75,83)(76,85)(78,95)(79,93)(80,94)(81,91)(82,88)(86,92)(89,100)(90,101)(96,99)(97,98);(54,55)(56,59)(57,60)(58,61)(62,65)(63,66)(64,68)(67,69)(70,71,76,80)(72,81,85,93)(73,86,90,96)(74,91,75,79)(77,84,94,83)(78,88,97,89)(82,99,100,92)(87,98,101,95)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,c^b=cf,d^b=dg,f^b=fg,i^b=i^52,d^c=dh,e^c=eg,f^c=fg,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 70196);