Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7289 |
184 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 6784 |
A minimal faithful permutation representation — 2 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)(54,56)(55,59,61,62)(57,64)(58,63)(60,67,68,69)(65,66)(70,72,74,83,87,98,88,99,76,85,73,82,75,84,90,100)(71,77,78,81,91,95,89,101,80,93,94,97,79,92,86,96);(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)(54,55,57,60,58,61,65,68)(56,62,64,69,63,59,66,67)(70,71)(72,81)(73,86)(74,89)(75,91)(76,80)(77,82)(78,88)(79,87)(83,93)(84,101)(85,97)(90,94)(92,100)(95,99)(96,98)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=fh,f^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fh,i^a=i^52,c^b=cg,i^b=i^521514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56796);