Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#13183527 |
| derived, Hall | #89205 ⋊ C4×C13 |
| Hall | C13×#89205 ⋊ C4 |
| Hall | C72×C13 ⋊ Dic9 |
| Sylow | C72 ⋊ C13×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | #11725071 |
| commutator, hypocenter | #89205 | C4×C13 |
| Frattini | C2×C3 | C13×#64418 |
| Fitting, socle, prime radical | C2×C3×C72×C13 | D3 |
| cosocle | C2×#89205 | C2×C13 |
| LCS | G ▷ #89205 | |
| UCS | C1 ◁ C2×C13 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3276 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 322);