Finite Group DatabasebetaFinite Group Databasebeta| order | 30723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#14584115 |
| Fitting, socle, Hall | C72×C11×C19 ⋊ C3 |
| derived, Hall | C72×C19 ⋊ C3×C11 |
| Hall | C72×C11 ⋊ C19⋊C3 |
| Hall | C11×C19 ⋊ #3861 |
| Sylow | C72 ⋊ C11×C19⋊C3 |
| Sylow | C19 ⋊ C11×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #14584115 |
| commutator, cosocle, hypocenter | C72×C19 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C11 | |
80 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, 12);