Finite Group DatabasebetaFinite Group Databasebeta| order | 12030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C401⋊C5 |
| unambiguous semidirect product | (C2×C401)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C3×C401)⋊C5 |
| Fitting, socle, Hall | C2×C3×C401 ⋊ C5 |
| derived, Sylow | C401 ⋊ C2×C3×C5 |
| Hall | C3×C401 ⋊ C2×C5 |
| Hall | C2×C401 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C401⋊C5 |
| commutator, cosocle, hypocenter | C401 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C401 | C5 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
510 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C401⋊C5, C3×Dic401⋊C5, Dic3×C401⋊C5, … |
| maximal normal subgroup of | C3×C4×C401⋊C5, C3×Dic401⋊C5, Dic3×C401⋊C5, … |
| maximal quotient of | C3×C4×C401⋊C5, C22×C3×C401⋊C5, C2×C9×C401⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12030, 2);