Finite Group DatabasebetaFinite Group Databasebeta| order | 3920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C7 |
| direct product | C22×D5×C7⋊D7 |
| Fitting, socle | C22×C5×C72 ⋊ C22 |
| derived, Hall | C5×C72 ⋊ C24 |
| Sylow | C72 ⋊ C23×D5 |
| Sylow | C5 ⋊ C23×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×C7⋊D7 |
| commutator, cosocle, hypocenter | C5×C72 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C72 | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C22 | |
1340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 980 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×AGL(1,𝔽5)×C7⋊D7, C22×D5×#64424, D5×#11716115, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×C7⋊D7, C22×D5×#64424, D5×#11716115, … |
Past the SmallGroups library coverage — no SmallGroups id.