Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#21439611 |
| Fitting, socle | C3×C72×C13 ⋊ C22×C3 |
| derived, Hall | C72×C13 ⋊ C22×C32 |
| Hall | C3×#14274262 ⋊ C22 |
| Hall | (C7⋊D7)⋊D13 ⋊ C32 |
| Sylow | C72 ⋊ C2×C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×#64423⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #21439611 |
| commutator, cosocle, hypocenter | C72×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
312 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 546 |
213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1043);