Finite Group DatabasebetaFinite Group Databasebeta| order | 27462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D199⋊C3 |
| unambiguous semidirect product | D199⋊(C3×C23) |
| unambiguous semidirect product | (C199⋊C3)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D199)⋊C3 |
| Fitting, socle, Hall | C23×C199 ⋊ C2×C3 |
| derived, Sylow | C199 ⋊ C2×C3×C23 |
| Hall | C23×C199⋊C3 ⋊ C2 |
| Hall | C23×D199 ⋊ C3 |
| Hall | C199⋊C3 ⋊ C2×C23 |
| Hall | D199 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D199⋊C3 |
| commutator, cosocle, hypocenter | C199 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C199 | C2×C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4577 |
897 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27462, 10);