Finite Group DatabasebetaFinite Group Databasebeta| order | 10560 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C23 |
| direct product | C11⋊C5×#5934 |
| Fitting | C11×H(5,𝔽2) ⋊ C5×D3 |
| derived | C11×#997 ⋊ C2×C5 |
| Hall | C11×#5934 ⋊ C5 |
| Sylow | C11 ⋊ C5×#5934 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊C5×#1020 |
| commutator, cosocle, hypocenter | C11×#997 | C2×C5 |
| Fitting | C11×H(5,𝔽2) | C5×D3 |
| socle | C2×C11 | C5×#1020 |
| LCS | G ▷ C11×#997 | |
| UCS | C1 ◁ C2 | |
392 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 88 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#5934 |
| maximal normal subgroup of | AGL(1,𝔽11)×#5934 |
Past the SmallGroups library coverage — no SmallGroups id.