Finite Group DatabasebetaFinite Group Databasebeta| order | 5280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C23 |
| direct product | C11⋊C5×#1020 |
| Fitting, socle | C24×C11 ⋊ C5×D3 |
| derived | C11×C22⋊A4 ⋊ C2×C5 |
| Hall | C11×#1020 ⋊ C5 |
| Sylow | C11 ⋊ C5×#1020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×C22⋊A4 | C2×C5 |
| Fitting, socle | C24×C11 | C5×D3 |
| LCS | G ▷ C11×C22⋊A4 | |
| UCS | C1 | |
224 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
70 conjugacy classes — view the full character table.
| maximal subgroup of | #1020×AGL(1,𝔽11), C11⋊C5×A4⋊S4 |
| maximal normal subgroup of | #1020×AGL(1,𝔽11) |
| maximal quotient of | C11⋊C5×#5935, C11⋊C5×#5934 |
Past the SmallGroups library coverage — no SmallGroups id.