Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #8705 |
486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 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)(54,56,57,60)(55,59,58,61)(62,65)(63,68)(64,70)(66,73)(67,74)(69,72)(71,77)(75,76)(80,86)(83,89)(87,92)(90,93);(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)(55,58)(59,61)(62,64,66,71)(63,67,69,75)(65,70,73,77)(68,74,72,76)(78,80,82,86)(79,83,85,89)(81,87,88,92)(84,90,91,93);(54,55)(56,59)(57,58)(60,61)(62,63)(64,67)(65,72,73,68)(66,69)(70,76,77,74)(71,75)(78,79,81,84,82,85,88,91)(80,83,87,90,86,89,92,93)Polycyclic presentation:
2^8,53|a^2=f,b^2=gh,c^2=d,f^2=h,b^a=bd,c^a=ce,e^a=eg,c^b=ch,i^b=i^52,f^c=fg1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62911);