Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #9153 |
586 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 127 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(55,57)(58,61,62,69)(59,64,65,73)(60,66,67,68)(63,70,71,72)(76,84)(80,88)(83,89)(85,86);(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)(58,60)(59,63,65,71)(61,68)(62,67)(64,72,73,70)(66,69)(74,76)(75,80,82,88)(77,85)(78,86)(79,84)(81,83,87,89);(54,55)(56,57)(58,59)(60,63,67,71)(61,64)(62,65)(66,70,68,72)(69,73)(74,75,78,81,79,82,77,87)(76,83,86,88,84,89,85,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=h,d^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,c^b=cg,d^b=dh,f^b=fh,i^b=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 65331);