Finite Group DatabasebetaFinite Group Databasebeta| order | 33813 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C17 |
| direct product | C13⋊C3×C172⋊C3 |
| unambiguous semidirect product | (C13⋊(C172⋊C3))⋊C3 |
| unambiguous semidirect product | (C172×C13⋊C3)⋊C3 |
| unambiguous semidirect product | (C13×C172⋊C3)⋊C3 |
| Fitting, socle, derived, Hall | C13×C172 ⋊ C32 |
| Sylow | C172 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C172⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C172 | C32 |
| LCS | G ▷ C13×C172 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 663 |
693 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33813, 11);