Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#11759813 |
| Fitting, socle, Hall | C132×C23 ⋊ D3 |
| derived, Hall | #92789 ⋊ C2×C23 |
| Hall | C23×#92789 ⋊ C2 |
| Sylow | C132 ⋊ D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11759813 |
| commutator, cosocle, hypocenter | #92789 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C132×C23 | D3 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C23 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 598 |
1127 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 14);