Finite Group DatabasebetaFinite Group Databasebeta| order | 33774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D433⋊C3 |
| unambiguous semidirect product | D433⋊(C3×C13) |
| unambiguous semidirect product | (C433⋊C3)⋊(C2×C13) |
| Fitting, socle, Hall | C13×C433 ⋊ C2×C3 |
| derived, Sylow | C433 ⋊ C2×C3×C13 |
| Hall | C13×C433⋊C3 ⋊ C2 |
| Hall | C13×D433 ⋊ C3 |
| Hall | C433⋊C3 ⋊ C2×C13 |
| Hall | D433 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D433⋊C3 |
| commutator, cosocle, hypocenter | C433 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C433 | C2×C3 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5629 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33774, 13);