Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12169 |
342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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:
(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)(54,56,57,60)(55,58,59,61)(62,64)(63,69)(65,79)(66,76)(67,77)(68,83)(70,90)(71,87)(72,88)(73,82)(74,81)(75,80)(78,92)(84,86)(85,93)(89,91);(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)(56,58)(57,59)(60,61)(63,68)(65,78)(66,80)(69,83)(70,71)(72,85)(73,86)(74,91)(75,76)(79,92)(81,89)(82,84)(87,90)(88,93);(58,61)(62,63,67,72)(64,73,77,87)(65,68,81,85)(66,82,80,71)(69,76,88,75)(70,89,84,78)(74,86,79,90)(83,92,93,91)Polycyclic presentation:
2^8,53|a^2=h,c^2=gh,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,d^b=df,e^b=eg,f^b=fh,d^c=dg,e^c=eh,i^c=i^52785 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 82068);