Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×D33 |
| Fitting, socle | C22×C3×C5×C11 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C23×C5 |
| Hall | C3×C5×C11 ⋊ C23 |
| Hall | C5×C11 ⋊ C22×D3 |
| Hall | C3×C5 ⋊ C22×D11 |
| Sylow | C11 ⋊ C22×C5×D3 |
| Sylow | C3 ⋊ C22×C5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C5×C11 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C22×C5 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 660 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 178);