Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, derived, Hall | Q8×C11 ⋊ C3×C5 |
| Hall | Q8×C11⋊C5 ⋊ C3 |
| Hall | C11×SL(2,𝔽3) ⋊ C5 |
| Sylow | C11 ⋊ C5×SL(2,𝔽3) |
| Sylow | Q8 ⋊ C3×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×C11⋊C5 |
| commutator, Fitting, cosocle, hypocenter | Q8×C11 | C3×C5 |
| socle | C2×C11 | C5×A4 |
| LCS | G ▷ Q8×C11 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
49 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#997, SL(2,𝔽3)×AGL(1,𝔽11), GL(2,𝔽3)×C11⋊C5, … |
| maximal normal subgroup of | SL(2,𝔽3)×AGL(1,𝔽11), GL(2,𝔽3)×C11⋊C5, #72222644 |
| maximal quotient of | C11⋊C5×PSU(3,𝔽2)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 22);