Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×#66526⋊C2 |
| unambiguous semidirect product | #66526⋊(C22×C23) |
| unambiguous semidirect product | (C2×#66526)⋊(C2×C23) |
| Fitting, socle | C2×C23×C37 ⋊ C2×C9 |
| derived, Sylow | C37 ⋊ C22×C9×C23 |
| Hall | C23×#66526 ⋊ C22 |
| Hall | C2×C23×D37 ⋊ C9 |
| Hall | C23×C37 ⋊ C22×C9 |
| Hall | #66526 ⋊ C22×C23 |
| Hall | C2×D37 ⋊ C9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | #66526⋊C2 |
| commutator, hypocenter | C37 | C22×C9×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C37 | C2×C9 |
| prime radical | C2×C23×D37⋊C3 | C3 |
| cosocle | C37⋊C3 | C22×C3×C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C23 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1702 |
920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 69);