Finite Group DatabasebetaFinite Group Databasebeta| order | 23022 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#26040240 |
| derived, Sylow | C1279 ⋊ C2×C9 |
| Hall | C2×C1279 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C1279⋊C3 |
| commutator, hypocenter | C1279 | C2×C9 |
| Frattini | C3 | C2×C1279⋊C3 |
| Fitting, socle, prime radical | C2×C3×C1279 | C3 |
| cosocle | C3×C1279 | C2×C3 |
| LCS | G ▷ C1279 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23022 |
2574 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23022, 3);