Finite Group DatabasebetaFinite Group Databasebeta| order | 11760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×AGL(1,𝔽5)×#3861 |
| Fitting, socle | C22×C5×C72 ⋊ C3×C4 |
| derived, Hall | C5×C72 ⋊ C22×C3×C4 |
| Hall | C22×C72×AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×#3861 ⋊ C22×C4 |
| Sylow | C72 ⋊ C22×C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C4×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽5)×#3861 |
| commutator, hypocenter | C5×C72 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C72 | C3×C4 |
| prime radical | C22×D5×#3861 | C2 |
| cosocle | C72×D5 | C23×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C22 | |
1080 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 352 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 980 |
380 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×AGL(1,𝔽5)×#64424, AGL(1,𝔽5)×#11924207 |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#64424, AGL(1,𝔽5)×#11924207 |
Past the SmallGroups library coverage — no SmallGroups id.