Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic851 |
| unambiguous semidirect product | C23⋊(C9×Dic37) |
| derived, Hall | C23×C37 ⋊ C4×C9 |
| Hall | C9×C23×C37 ⋊ C4 |
| Hall | C9×C37 ⋊ Dic23 |
| Hall | C9×C23 ⋊ Dic37 |
| Sylow | C37 ⋊ C9×Dic23 |
| Sylow | C23 ⋊ C9×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D851 |
| commutator, hypocenter | C23×C37 | C4×C9 |
| Frattini | C2×C3 | C3×D851 |
| Fitting | C2×C9×C23×C37 | C2 |
| socle, prime radical, cosocle | C2×C3×C23×C37 | C2×C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C2×C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30636 |
7686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 5);