Finite Group DatabasebetaFinite Group Databasebeta| order | 24548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C361 · Schur multiplier (H2) = C1 |
| direct product | #595×C361 |
| Fitting, Hall | C17×C361 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C361 | #595 |
| commutator, hypocenter | C17 | C4×C361 |
| Frattini | C19 | C19×#595 |
| Fitting | C17×C361 | C4 |
| socle | C17×C19 | C4×C19 |
| prime radical, cosocle | C19×D17 | C2×C19 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C361 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6137 |
2888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24548, 6);