Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D851 |
| unambiguous semidirect product | (C2×C23)⋊(C32×D37) |
| Fitting, socle | C2×C32×C23×C37 ⋊ C2 |
| derived, Hall | C23×C37 ⋊ C22×C32 |
| Hall | C32×C23×C37 ⋊ C22 |
| Hall | C32×C37 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C32×D23 |
| Sylow | C23 ⋊ C2×C32×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D851 |
| commutator, cosocle, hypocenter | C23×C37 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C23×C37 | C2 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15318 |
7686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 133);