Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of C3⋊(C3⋊D15) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3⋊(C3⋊D15) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊D15) |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊(C3⋊D3)) |
| Fitting, socle | C2×C33×C5 ⋊ C2 |
| derived, Hall | C33×C5 ⋊ C22 |
| Sylow | C33 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×C3⋊(C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊D15) |
| commutator, cosocle, hypocenter | C33×C5 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C2 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | #11762061, #11762063, #11762064, … |
| maximal normal subgroup of | #11762061, #11762063, #11762064, … |
| maximal quotient of | #11762133, C4×C3⋊(C3⋊D15), C4⋊(C3⋊(C3⋊D15)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 118);