Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived | C22×C11 ⋊ C2×C3×C5 |
| Hall | C22×AGL(1,𝔽11) ⋊ C3 |
| Hall | A4×D11 ⋊ C5 |
| Hall | C22×D11 ⋊ C3×C5 |
| Hall | C11⋊C5 ⋊ C2×A4 |
| Sylow | C11 ⋊ C2×C5×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C11 | C2×C3×C5 |
| LCS | G ▷ C22×C11 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 44 |
44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 141);