Finite Group DatabasebetaFinite Group Databasebeta| order | 11760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×#64423⋊C2 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C22×C3×C4 |
| Hall | D72×AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×#3861 ⋊ C22×C4 |
| Hall | #3861 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C72 ⋊ C22×C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#64423⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72 | C22×C3×C4 |
| prime radical | D5×#64423⋊C2 | C2 |
| cosocle | C72×D5 | C23×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
528 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
95 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.