Finite Group DatabasebetaFinite Group Databasebeta| order | 24548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×D192 |
| unambiguous semidirect product | (C19×D19)⋊(C2×C17) |
| unambiguous semidirect product | (C19⋊D19)⋊(C2×C17) |
| Fitting, socle, Hall | C17×C192 ⋊ C22 |
| derived, Sylow | C192 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D192 |
| commutator, cosocle, hypocenter | C192 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C192 | C22 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C17 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 646 |
2057 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24548, 20);