Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived | C3×C72×C13 ⋊ C22×C3 |
| Hall | C3×#14274263 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×C3×D3 |
| Sylow | C72 ⋊ D3×D13⋊C3 |
| Sylow | C13 ⋊ C2×C3⋊#64424 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 1911 |
A minimal faithful permutation representation — 3 generators on 30 points:
(1,2,8)(3,9,13)(4,6,11)(5,12,7)(15,16)(18,21,22,19,20,23)(25,28,29,26,27,30);(2,3)(4,6)(5,9)(7,8)(10,12)(11,13)(14,15,16)(24,25,27,30,29,28,26);(17,18,20,23,22,21,19)Polycyclic presentation:
2^2,3^2,7^2,13|g^a=g^12,d^b=d^2,e^b=e^6,f^b=f^6,e^c=e^2,f^c=f^2,g^c=g^3216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1210);