Finite Group DatabasebetaFinite Group Databasebeta| order | 7230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D3×C241⋊C5 |
| unambiguous semidirect product | C3⋊(C2×C241⋊C5) |
| unambiguous semidirect product | (D3×C241)⋊C5 |
| Fitting, socle, derived, Hall | C3×C241 ⋊ C2×C5 |
| Hall | C3×C241⋊C5 ⋊ C2 |
| Hall | D3×C241 ⋊ C5 |
| Sylow | C241 ⋊ C5×D3 |
| Sylow | C3 ⋊ C2×C241⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C241 | C2×C5 |
| LCS | G ▷ C3×C241 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
159 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D241⋊C5, C2×D3×C241⋊C5, D9×C241⋊C5, … |
| maximal normal subgroup of | D3×D241⋊C5, C2×D3×C241⋊C5, D3×(C241⋊C3)⋊C5, … |
| maximal quotient of | Dic3×C241⋊C5, C2×D3×C241⋊C5, D9×C241⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7230, 13);