Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×D5×C11 |
| unambiguous semidirect product | (C5×D3)⋊(C22×C11) |
| unambiguous semidirect product | (C3×D5)⋊(C22×C11) |
| unambiguous semidirect product | D15⋊(C22×C11) |
| Fitting, socle | C2×C3×C5×C11 ⋊ C22 |
| derived, Hall | C3×C5 ⋊ C23×C11 |
| Hall | C3×C5×C11 ⋊ C23 |
| Hall | C5×C11 ⋊ C22×D3 |
| Hall | C3×C11 ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×D3×C11 |
| Sylow | C3 ⋊ C22×D5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D3×D5 |
| commutator, cosocle, hypocenter | C3×C5 | C23×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C11 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C11 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 169);