Finite Group DatabasebetaFinite Group Databasebeta| order | 27462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C199 · Schur multiplier (H2) = C1 |
| direct product | D69×C199 |
| unambiguous semidirect product | C3⋊(D23×C199) |
| unambiguous semidirect product | C23⋊(D3×C199) |
| Fitting, socle, Hall | C3×C23×C199 ⋊ C2 |
| derived, Hall | C3×C23 ⋊ C2×C199 |
| Hall | C23×C199 ⋊ D3 |
| Hall | C3×C199 ⋊ D23 |
| Sylow | C23 ⋊ D3×C199 |
| Sylow | C3 ⋊ D23×C199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C199 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C2×C199 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C199 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C199 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13731 |
7164 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27462, 8);