Finite Group DatabasebetaFinite Group Databasebeta| order | 33813 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C3×C17 |
| direct product | C3×C13×C172⋊C3 |
| unambiguous semidirect product | C172⋊(C32×C13) |
| unambiguous semidirect product | (C3×C172)⋊(C3×C13) |
| Fitting, socle | C3×C13×C172 ⋊ C3 |
| derived, Sylow | C172 ⋊ C32×C13 |
| Hall | C13×C172 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C172⋊C3 |
| commutator, cosocle, hypocenter | C172 | C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C172 | C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C3×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1989 |
3861 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33813, 13);