Finite Group DatabasebetaFinite Group Databasebeta| order | 24453 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×#4296 |
| Fitting, socle, Hall | C11×C13×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C9×C11×C13 |
| Hall | C13×C19 ⋊ C9×C11 |
| Hall | C11×C19 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | #4296 |
| commutator, hypocenter | C19 | C9×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C19 | C9 |
| prime radical | C11×C13×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C3×C11×C13 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C11×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2717 |
1573 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24453, 7);