Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D33 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D11) |
| Fitting, socle | C2×C3×C5×C11 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C22×C5 |
| Hall | C3×C5×C11 ⋊ C22 |
| Hall | C5×C11 ⋊ C2×D3 |
| Hall | C3×C5 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C2×C5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C11 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D33⋊C4, C5×#63141, C5×#63142, … |
| maximal normal subgroup of | C5×D33⋊C4, C5×#63141, C5×#63142, … |
| maximal quotient of | C5×Dic66, C4×C5×D33, C5×D132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 37);