Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D23×#66524⋊C2 |
| unambiguous semidirect product | (C23×#66524⋊C2)⋊C2 |
| unambiguous semidirect product | (D23×#66524)⋊C2 |
| unambiguous semidirect product | (C23⋊(#66524⋊C2))⋊C2 |
| derived, Hall | C23×C37 ⋊ C22×C9 |
| Hall | C23×#66524 ⋊ C22 |
| Hall | D23×D37 ⋊ C9 |
| Hall | #66524 ⋊ C2×D23 |
| Sylow | C37 ⋊ C2×C9×D23 |
| Sylow | C23 ⋊ C2×#66524⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D23×D37⋊C3 |
| commutator, hypocenter | C23×C37 | C22×C9 |
| Fitting, socle, cosocle | C3×C23×C37 | C22×C3 |
| prime radical | C3×D23×D37 | C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7659 |
468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 16);