Finite Group DatabasebetaFinite Group Databasebeta| order | 23126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C2×C373⋊C31 |
| unambiguous semidirect product | (C2×C373)⋊C31 |
| Fitting, socle, Hall | C2×C373 ⋊ C31 |
| derived, Sylow | C373 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C373⋊C31 |
| commutator, cosocle, hypocenter | C373 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C373 | C31 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 746 |
86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23126, 2);