Finite Group DatabasebetaFinite Group Databasebeta| order | 33154 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1507 |
| unambiguous semidirect product | C11⋊(C11×D137) |
| unambiguous semidirect product | C137⋊(C11×D11) |
| Fitting, socle, Hall | C112×C137 ⋊ C2 |
| derived | C11×C137 ⋊ C2×C11 |
| Sylow | C137 ⋊ C11×D11 |
| Sylow | C112 ⋊ D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1507 |
| commutator, cosocle, hypocenter | C11×C137 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C137 | C2 |
| LCS | G ▷ C11×C137 | |
| UCS | C1 ◁ C11 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3014 |
8305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33154, 8);