Finite Group DatabasebetaFinite Group Databasebeta| order | 11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×C5⋊AGL(1,𝔽11) |
| Fitting, socle, derived | C52×C11 ⋊ C2×C4×C5 |
| Hall | C52×C11⋊C5 ⋊ C2×C4 |
| Sylow | C11 ⋊ C5×D5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11 | C2×C4×C5 |
| prime radical | D5×C5⋊AGL(1,𝔽11) | C2 |
| cosocle | C5×D5×C11 | C22×C5 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 | |
176 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 220 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(1,𝔽5)×AGL(1,𝔽11) |
| maximal normal subgroup of | D5×AGL(1,𝔽5)×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.