Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊Dic111 |
| unambiguous semidirect product | C3⋊(C23×Dic111) |
| derived, Hall | C32×C37 ⋊ C4×C23 |
| Hall | C32×C23×C37 ⋊ C4 |
| Hall | C23×C37 ⋊ C3⋊Dic3 |
| Hall | C32×C23 ⋊ Dic37 |
| Sylow | C37 ⋊ C23×C3⋊Dic3 |
| Sylow | C32 ⋊ C23×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | C3⋊D111 |
| commutator, hypocenter | C32×C37 | C4×C23 |
| Frattini | C2 | C23×C3⋊D111 |
| Fitting, socle, prime radical | C2×C32×C23×C37 | C2 |
| cosocle | C2×C32×C37 | C2×C23 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 ◁ C2×C23 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30636 |
7728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 56);