Finite Group DatabasebetaFinite Group Databasebeta| order | 23012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D523 |
| unambiguous semidirect product | (D11×C523)⋊C2 |
| unambiguous semidirect product | (C11×D523)⋊C2 |
| unambiguous semidirect product | D5753⋊C2 |
| Fitting, socle, derived, Hall | C11×C523 ⋊ C22 |
| Sylow | C523 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D523 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C523 | C22 |
| LCS | G ▷ C11×C523 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5753 |
1841 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23012, 6);