Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C5×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C2×C3⋊D3)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C3⋊D3)⋊C3 |
| Fitting | C2×C5×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C22×C3×C5 |
| Hall | C5×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C32 | C22×C3×C5 |
| Frattini | C3 | C2×C3×C5×D3 |
| Fitting | C2×C5×H(3,𝔽3) | C2 |
| socle | C2×C3×C5 | C3×D3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C5 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×(C3⋊D3)⋊C3, #67140⋊C3, #67138⋊C3, … |
| maximal normal subgroup of | Dic5×(C3⋊D3)⋊C3, #67140⋊C3, #67138⋊C3, … |
| maximal quotient of | C5×#634⋊C3, C4×C5×(C3⋊D3)⋊C3, C5×C4⋊((C3⋊D3)⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 67);