Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9304 |
436 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 113 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(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)(54,56,58,57)(55,60,61,59)(62,65,67,77)(63,69,70,84)(64,72,73,87)(66,79,80,76)(68,81,83,92)(71,85,78,75)(74,91,89,88)(82,93,90,86);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,55,57,59,58,61,56,60)(62,64)(63,68,70,83)(65,72)(66,74)(67,73)(69,81,84,92)(71,82,78,90)(75,86,85,93)(76,88)(77,87)(79,91)(80,89);(55,59)(56,57)(60,61)(62,63)(64,68,73,83)(65,75)(66,78)(67,70)(69,76)(71,80)(72,86,87,93)(74,90,89,82)(77,85)(79,84)(81,91,92,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fh,e^c=eh,i^c=i^52881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66327);