Finite Group DatabasebetaFinite Group Databasebeta| order | 33154 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×D137 |
| unambiguous semidirect product | C137⋊(C2×C121) |
| Fitting, Hall | C121×C137 ⋊ C2 |
| derived, Sylow | C137 ⋊ C2×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D137 |
| commutator, hypocenter | C137 | C2×C121 |
| Frattini | C11 | C11×D137 |
| Fitting | C121×C137 | C2 |
| socle, cosocle | C11×C137 | C2×C11 |
| prime radical | C11×D137 | C11 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C121 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16577 |
8470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33154, 3);