Finite Group DatabasebetaFinite Group Databasebeta| order | 11760 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×#10596873 |
| derived, Hall | C5×C72 ⋊ C3×C42 |
| Hall | C7×AGL(1,𝔽5)×Dic7 ⋊ C3 |
| Hall | C5×#3861 ⋊ C42 |
| Hall | #3861 ⋊ C4×AGL(1,𝔽5) |
| Sylow | C72 ⋊ C3×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#10596873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×#64423 |
| commutator, hypocenter | C5×C72 | C3×C42 |
| Fitting, socle | C2×C5×C72 | C2×C3×C4 |
| prime radical | C2×D5×#3861 | C22 |
| cosocle | C2×C72×D5 | C22×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#11924174, AGL(1,𝔽5)×#11924207, AGL(1,𝔽5)×#11924176 |
| maximal normal subgroup of | AGL(1,𝔽5)×#11924174, AGL(1,𝔽5)×#11924207, AGL(1,𝔽5)×#11924176 |
Past the SmallGroups library coverage — no SmallGroups id.