Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D3×C23×D111 |
| unambiguous semidirect product | (C3×D3)⋊(C23×D37) |
| unambiguous semidirect product | (D3×C37)⋊(D3×C23) |
| Fitting, socle, Hall | C32×C23×C37 ⋊ C22 |
| derived, Hall | C32×C37 ⋊ C22×C23 |
| Hall | C23×C37 ⋊ D32 |
| Hall | C32×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ D32×C23 |
| Sylow | C32 ⋊ C2×C23×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D111 |
| commutator, cosocle, hypocenter | C32×C37 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C37 | C22 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 ◁ C23 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5106 |
3933 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 111);