Finite Group DatabasebetaFinite Group Databasebeta| order | 30723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#14584107 |
| Fitting, Hall | C11×C19×C49 ⋊ C3 |
| derived, Hall | C19×C49 ⋊ C3×C11 |
| Hall | C11×C49 ⋊ C19⋊C3 |
| Hall | C11×C19 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C11×C19⋊C3 |
| Sylow | C19 ⋊ C11×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #14584107 |
| commutator, cosocle, hypocenter | C19×C49 | C3×C11 |
| Frattini | C7 | C11×#87704 |
| Fitting | C11×C19×C49 | C3 |
| socle | C7×C11×C19 | ΓL(1,𝔽8) |
| LCS | G ▷ C19×C49 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10241 |
3443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30723, 4);