Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C11×A4 |
| unambiguous semidirect product | C23⋊(C3×C5×C11) |
| unambiguous semidirect product | (C23×C5)⋊(C3×C11) |
| unambiguous semidirect product | (C23×C5×C11)⋊C3 |
| Fitting, socle, Hall | C23×C5×C11 ⋊ C3 |
| derived | C22 ⋊ C2×C3×C5×C11 |
| Hall | C23×C11 ⋊ C3×C5 |
| Hall | C23×C5 ⋊ C3×C11 |
| Sylow | C23 ⋊ C3×C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | A4 |
| commutator, cosocle, hypocenter | C22 | C2×C3×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C23×C5×C11 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C5×C11 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 330 |
440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 173);