Finite Group DatabasebetaFinite Group Databasebeta| order | 17460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D15×D97⋊C3 |
| unambiguous semidirect product | D97⋊(C3×D15) |
| unambiguous semidirect product | (C3×D97⋊C3)⋊D5 |
| unambiguous semidirect product | (C5×D97⋊C3)⋊D3 |
| unambiguous semidirect product | (D15×D97)⋊C3 |
| Fitting, socle, derived | C3×C5×C97 ⋊ C22×C3 |
| Hall | C3×C5×C97⋊C3 ⋊ C22 |
| Hall | C3×C97⋊C3 ⋊ C2×D5 |
| Hall | C5×C97 ⋊ C2×C3×D3 |
| Sylow | C97 ⋊ C2×C3×D15 |
| Sylow | C5 ⋊ D3×D97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C97 | C22×C3 |
| LCS | G ▷ C3×C5×C97 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1455 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17460, 88);