Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C13×D7×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C32×C13×D7) |
| Fitting, socle | C3×C72×C13 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C22×C32×C13 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C13×D72 ⋊ C32 |
| Hall | C72×C13 ⋊ C22×C32 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C22×C13 |
| Hall | D72 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D7×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C72 | C22×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C13 | |
248 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1638 |
1365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1002);