Finite Group DatabasebetaFinite Group Databasebeta| order | 33902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×AGL(1,𝔽23) |
| unambiguous semidirect product | D23⋊(C11×C67) |
| unambiguous semidirect product | (C23⋊C11)⋊(C2×C67) |
| Fitting, socle, Hall | C23×C67 ⋊ C2×C11 |
| derived, Sylow | C23 ⋊ C2×C11×C67 |
| Hall | C67×C23⋊C11 ⋊ C2 |
| Hall | D23×C67 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×C67 |
| Hall | D23 ⋊ C11×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23 | C2×C11×C67 |
| Frattini | C1 | G |
| Fitting, socle | C23×C67 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1541 |
1541 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33902, 34);