Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C3⋊D3×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×A5 |
| unambiguous semidirect product | C3⋊(D3×A5) |
| Fitting | C32 ⋊ C2×A5 |
| socle, derived | C32×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C32×A5 | C2 |
| Fitting, cosocle | C32 | C2×A5 |
| LCS | G ▷ C32×A5 | |
| UCS | C1 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | #157×A5, D32×A5, C3⋊D3×S5, … |
| maximal normal subgroup of | #157×A5, D32×A5, C3⋊D3×S5, … |
| maximal quotient of | C3⋊Dic3×A5, C3⋊D3×SL(2,𝔽5), #72228179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 491);