Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1381 ⋊ C2 |
| Sylow | C53 ⋊ #13144 |
334 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,60,61,70,73,85,80,86,63,72,74,69,62,71,65,79)(59,66,64,75,76,87,84,89,68,83,78,82,67,81,77,88);(54,56,57,55)(58,59,65,77,62,67,74,78,63,68,80,84,73,76,61,64)(60,66,79,88,71,81,69,82,72,83,86,89,85,87,70,75);(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)(54,55,57,56)(59,64)(60,69)(61,65)(62,73)(66,81)(67,84)(68,78)(70,72)(71,79)(74,80)(75,82)(76,77)(83,87)(85,86)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=d,d^2=gh,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^52,e^c=eh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87464);