Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #9976 |
716 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 85 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)(55,58)(57,60)(59,61)(62,65,68,82)(63,70,72,89)(64,74,77,92)(66,80,67,81)(69,84,86,91)(71,88,83,78)(73,90,85,87)(75,79,76,93);(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)(58,61)(62,64)(63,69)(65,79)(66,76)(67,75)(68,77)(70,87)(71,85)(72,86)(73,83)(74,80)(78,84)(81,92)(82,93)(88,91)(89,90);(54,55)(56,58)(57,59)(60,61)(62,63,68,72)(64,73,77,85)(65,78,82,88)(66,83,67,71)(69,76,86,75)(70,80,89,81)(74,91,92,84)(79,90,93,87)Polycyclic presentation:
2^8,53|a^2=g,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,c^b=cf,d^b=dg,f^b=fg,d^c=dh,e^c=eg,f^c=fg,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 70177);