Finite Group DatabasebetaFinite Group Databasebeta| order | 16230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×(C541⋊C3)⋊C5 |
| unambiguous semidirect product | (C2×C541⋊C3)⋊C5 |
| unambiguous semidirect product | (C2×C541⋊C5)⋊C3 |
| Fitting, socle, Hall | C2×C541 ⋊ C3×C5 |
| derived, Sylow | C541 ⋊ C2×C3×C5 |
| Hall | C2×C541⋊C5 ⋊ C3 |
| Hall | C2×C541⋊C3 ⋊ C5 |
| Hall | C541⋊C5 ⋊ C2×C3 |
| Hall | C541⋊C3 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C541⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C541 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C541 | C3×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1082 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(C541⋊C3)⋊C5, (Dic541⋊C3)⋊C5, C2×(D541⋊C3)⋊C5, … |
| maximal normal subgroup of | C4×(C541⋊C3)⋊C5, (Dic541⋊C3)⋊C5, C2×(D541⋊C3)⋊C5, … |
| maximal quotient of | C4×(C541⋊C3)⋊C5, C22×(C541⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16230, 4);