Finite Group DatabasebetaFinite Group Databasebeta| order | 24140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C17⋊(D71⋊C5) |
| unambiguous semidirect product | (C2×C17)⋊(D71⋊C5) |
| unambiguous semidirect product | (C2×C71⋊C5)⋊D17 |
| unambiguous semidirect product | (C2×D1207)⋊C5 |
| Fitting, socle | C2×C17×C71 ⋊ C2×C5 |
| derived, Hall | C17×C71 ⋊ C22×C5 |
| Hall | C17×C71⋊C5 ⋊ C22 |
| Hall | C2×D1207 ⋊ C5 |
| Hall | C71⋊C5 ⋊ C2×D17 |
| Sylow | C71 ⋊ C2×C5×D17 |
| Sylow | C17 ⋊ C2×D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊(D71⋊C5) |
| commutator, cosocle, hypocenter | C17×C71 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C71 | C2×C5 |
| LCS | G ▷ C17×C71 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2414 |
338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24140, 18);