Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8679 |
350 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 107 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)(54,56,57,63)(55,60,59,68)(58,67,65,64)(61,69,66,62)(70,73,75,87)(71,77,79,85)(72,82,84,98)(74,86,81,95)(76,89,90,99)(78,91,88,100)(80,92,93,96)(83,97,94,101);(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)(55,59)(60,68)(61,66)(62,69)(70,72,81,94,75,84,74,83)(71,76,88,93,79,90,78,80)(73,82,95,101,87,98,86,97)(77,89,100,96,85,99,91,92);(54,55)(56,62)(57,59)(58,66)(60,64)(61,65)(63,69)(67,68)(70,71)(72,80)(73,85,87,77)(74,88)(75,79)(76,83)(78,81)(82,96,98,92)(84,93)(86,91,95,100)(89,97,99,101)(90,94)Polycyclic presentation:
2^8,53|a^2=f,b^2=dh,c^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^b=i^52,e^c=egh,f^c=fg,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62796);