Finite Group DatabasebetaFinite Group Databasebeta| order | 23230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D23×C101⋊C5 |
| unambiguous semidirect product | C23⋊(C2×C101⋊C5) |
| unambiguous semidirect product | (D23×C101)⋊C5 |
| Fitting, socle, derived, Hall | C23×C101 ⋊ C2×C5 |
| Hall | C23×C101⋊C5 ⋊ C2 |
| Hall | D23×C101 ⋊ C5 |
| Sylow | C101 ⋊ C5×D23 |
| Sylow | C23 ⋊ C2×C101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C101 | C2×C5 |
| LCS | G ▷ C23×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2323 |
325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23230, 11);