Finite Group DatabasebetaFinite Group Databasebeta| order | 30723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×#87704 |
| Fitting, socle, Hall | C72×C11×C19 ⋊ C3 |
| derived | C7×C19 ⋊ C3×C7×C11 |
| Hall | C72×C19 ⋊ C3×C11 |
| Hall | C72×C11 ⋊ C19⋊C3 |
| Hall | C11×C19 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C11×C19⋊C3 |
| Sylow | C19 ⋊ C7×C11×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | #87704 |
| commutator, cosocle, hypocenter | C7×C19 | C3×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C19 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C7×C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4389 |
3619 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30723, 9);