Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #3861⋊(C22⋊(C13⋊C3)) |
| Fitting, socle, derived, Hall | C22×C72×C13 ⋊ C32 |
| Hall | C72×C13 ⋊ C3×A4 |
| Hall | C22×C72 ⋊ C3×C13⋊C3 |
| Hall | C22×C13 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C72 ⋊ C3×C22⋊(C13⋊C3) |
| Sylow | C13 ⋊ #3861⋊A4 |
| Sylow | C22 ⋊ #3861⋊(C13⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C72×C13 | C32 |
| LCS | G ▷ C22×C72×C13 | |
| UCS | C1 | |
152 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 546 |
Polycyclic presentation:
3^2,2^2,7^2,13|c^a=d,d^a=cd,e^a=e^4,g^a=g^3,e^b=e^2,f^b=f^2348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1349);