Finite Group DatabasebetaFinite Group Databasebeta| order | 23012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic523 |
| unambiguous semidirect product | C523⋊(C4×C11) |
| derived, Sylow | C523 ⋊ C4×C11 |
| Hall | C11×C523 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D523 |
| commutator, hypocenter | C523 | C4×C11 |
| Frattini | C2 | C11×D523 |
| Fitting, socle, prime radical | C2×C11×C523 | C2 |
| cosocle | C2×C523 | C2×C11 |
| LCS | G ▷ C523 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23012 |
5786 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23012, 3);