Finite Group DatabasebetaFinite Group Databasebeta| order | 24548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C19 |
| direct product | C2×C17⋊(C19⋊D19) |
| unambiguous semidirect product | (C2×C17)⋊(C19⋊D19) |
| unambiguous semidirect product | (C2×C19)⋊D323 |
| Fitting, socle | C2×C17×C192 ⋊ C2 |
| derived, Hall | C17×C192 ⋊ C22 |
| Sylow | C192 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊(C19⋊D19) |
| commutator, cosocle, hypocenter | C17×C192 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C192 | C2 |
| LCS | G ▷ C17×C192 | |
| UCS | C1 ◁ C2 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12274 |
6140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24548, 34);