Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C5⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C5⋊((C3⋊D3)⋊C3) |
| Fitting | C22×C5×H(3,𝔽3) ⋊ C2 |
| derived | C32×C5 ⋊ C23×C3 |
| Hall | C5×H(3,𝔽3) ⋊ C23 |
| Sylow | H(3,𝔽3) ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×(C3⋊D3)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C32×C5 | C23×C3 |
| Frattini | C3 | C22×C3×D15 |
| Fitting | C22×C5×H(3,𝔽3) | C2 |
| socle | C22×C3×C5 | C3×D3 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 354);