Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D3×C13×D147 |
| unambiguous semidirect product | (C3×D3)⋊(C13×D49) |
| unambiguous semidirect product | (D3×C49)⋊(D3×C13) |
| Fitting, Hall | C32×C13×C49 ⋊ C22 |
| derived, Hall | C32×C49 ⋊ C22×C13 |
| Hall | C13×C49 ⋊ D32 |
| Hall | C32×C13 ⋊ C2×D49 |
| Sylow | C49 ⋊ D32×C13 |
| Sylow | C32 ⋊ C2×C13×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D3×D147 |
| commutator, cosocle, hypocenter | C32×C49 | C22×C13 |
| Frattini | C7 | D3×C13×D21 |
| Fitting | C32×C13×C49 | C22 |
| socle | C32×C7×C13 | C2×D7 |
| LCS | G ▷ C32×C49 | |
| UCS | C1 ◁ C13 | |
132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3822 |
2925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 235);