Finite Group DatabasebetaFinite Group Databasebeta| order | 13200 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | A4×AGL(1,𝔽5)×C11⋊C5 |
| Fitting, socle, derived | C22×C5×C11 ⋊ C3×C4×C5 |
| Hall | C22×AGL(1,𝔽5)×C11⋊C5 ⋊ C3 |
| Hall | C5×C11⋊C5 ⋊ C4×A4 |
| Sylow | C11 ⋊ C5×A4×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C5×C11 | C3×C4×C5 |
| prime radical | D5×A4×C11⋊C5 | C2 |
| cosocle | C22×D5×C11 | C2×C3×C5 |
| LCS | G ▷ C22×C5×C11 | |
| UCS | C1 | |
162 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 162 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 |
140 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.