Finite Group DatabasebetaFinite Group Databasebeta| order | 33756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Dic97⋊C3 |
| unambiguous semidirect product | Dic97⋊(C3×C29) |
| unambiguous semidirect product | (C29×Dic97)⋊C3 |
| derived, Sylow | C97 ⋊ C3×C4×C29 |
| Hall | C29×Dic97 ⋊ C3 |
| Hall | C29×C97⋊C3 ⋊ C4 |
| Hall | C29×C97 ⋊ C3×C4 |
| Hall | Dic97 ⋊ C3×C29 |
| Hall | C97⋊C3 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D97⋊C3 |
| commutator, hypocenter | C97 | C3×C4×C29 |
| Frattini | C2 | C29×D97⋊C3 |
| Fitting, socle | C2×C29×C97 | C2×C3 |
| prime radical | C2×C29×C97⋊C3 | C2 |
| cosocle | C2×C97 | C2×C3×C29 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11252 |
1276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33756, 10);