Finite Group DatabasebetaFinite Group Databasebeta| order | 11760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#72219858 |
| Fitting, socle | C2×C5×C72 ⋊ C2×C3×C4 |
| derived, Hall | C5×C72 ⋊ C22×C3×C4 |
| Hall | C2×(C7⋊AGL(1,𝔽5))⋊D7 ⋊ C3 |
| Hall | C5×#3861 ⋊ C22×C4 |
| Hall | #3861 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C72 ⋊ C22×C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#11924174 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72219858 |
| commutator, hypocenter | C5×C72 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72 | C2×C3×C4 |
| prime radical | C2×D5×#64424 | C2 |
| cosocle | C72×D5 | C23×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
624 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#64423⋊C2, AGL(1,𝔽5)×#11924174, #72243649, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#64423⋊C2, AGL(1,𝔽5)×#11924174, #72243649, … |
| maximal quotient of | #72243660 |
Past the SmallGroups library coverage — no SmallGroups id.