Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D3×D5×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| Fitting, socle, derived, Hall | C3×C5×C11 ⋊ C23 |
| Hall | C5×C11 ⋊ C22×D3 |
| Hall | C3×C11 ⋊ C22×D5 |
| Hall | C3×C5 ⋊ C22×D11 |
| Sylow | C11 ⋊ C2×D3×D5 |
| Sylow | C5 ⋊ C2×D3×D11 |
| Sylow | C3 ⋊ C2×D5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C11 | C23 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×D11, D3×D5×AGL(1,𝔽11) |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×D11, D3×D5×AGL(1,𝔽11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 153);