Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C3⋊(C3⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2×C33 |
| direct product | C5×C3⋊(C3⋊S4) |
| unambiguous semidirect product | C3⋊(C5×C3⋊S4) |
| unambiguous semidirect product | A4⋊(C5×C3⋊D3) |
| Fitting, socle | C22×C32×C5 ⋊ D3 |
| derived | C32×A4 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | C32×A4 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | D3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 ◁ C5 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 546);