Finite Group DatabasebetaFinite Group Databasebeta| order | 3920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C7 |
| direct product | C22×C7⋊(C7⋊AGL(1,𝔽5)) |
| Fitting, socle | C22×C5×C72 ⋊ C4 |
| derived, Hall | C5×C72 ⋊ C22×C4 |
| Sylow | C72 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C7⋊(C7⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C5×C72 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C72 | C4 |
| prime radical | C22×C72×D5 | C2 |
| cosocle | C72×D5 | C23 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C22 | |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 980 |
404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×AGL(1,𝔽5)×C7⋊D7, C22×#15668765, #72243505 |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×C7⋊D7, C22×#15668765, #72243505 |
Past the SmallGroups library coverage — no SmallGroups id.