Finite Group DatabasebetaFinite Group Databasebeta| order | 17460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#87604⋊C9 |
| unambiguous semidirect product | #87604⋊(C5×C9) |
| unambiguous semidirect product | (C5×#87604)⋊C9 |
| derived, Sylow | C97 ⋊ C4×C5×C9 |
| Hall | C5×C97⋊C9 ⋊ C4 |
| Hall | C5×#87604 ⋊ C9 |
| Hall | C97⋊C9 ⋊ C4×C5 |
| Hall | C5×C97 ⋊ C4×C9 |
| Hall | #87604 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #87604⋊C3 |
| commutator, hypocenter | C97 | C4×C5×C9 |
| Frattini | C3 | C5×#87604⋊C3 |
| Fitting, socle | C3×C5×C97 | C3×C4 |
| prime radical | C3×C5×D97 | C2×C3 |
| cosocle | C3×D97 | C2×C3×C5 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4365 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17460, 14);