Finite Group DatabasebetaFinite Group Databasebeta| order | 11760 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×D5×#64424 |
| Fitting, socle | C22×C5×C72 ⋊ C22×C3 |
| derived, Hall | C5×C72 ⋊ C24×C3 |
| Hall | C22×D5×C7⋊D7 ⋊ C3 |
| Hall | C5×#3861 ⋊ C24 |
| Hall | #3861 ⋊ C23×D5 |
| Sylow | C72 ⋊ C23×C3×D5 |
| Sylow | C5 ⋊ C23×#64424 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×#64424 |
| commutator, cosocle, hypocenter | C5×C72 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C72 | C22×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C22 | |
2680 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 2680 conjugacy classes of subgroups — too many to draw. Only its 355 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 980 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽5)×#64424, D5×#72210376, #72243660 |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#64424, D5×#72210376, #72243660 |
Past the SmallGroups library coverage — no SmallGroups id.