Finite Group DatabasebetaFinite Group Databasebeta| order | 30723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72×C11 · Schur multiplier (H2) = C7 |
| direct product | C72×C11×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C72×C11) |
| unambiguous semidirect product | (C11×C19)⋊(C3×C72) |
| Fitting, socle, Hall | C72×C11×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C72×C11 |
| Hall | C72×C19 ⋊ C3×C11 |
| Hall | C11×C19 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C11 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C72×C11 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C72×C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10241 |
4851 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30723, 7);