Finite Group DatabasebetaFinite Group Databasebeta| order | 3920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×(C7⋊AGL(1,𝔽5))⋊D7 |
| Fitting, socle | C2×C5×C72 ⋊ C2×C4 |
| derived, Hall | C5×C72 ⋊ C22×C4 |
| Sylow | C72 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#87639 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C7⋊AGL(1,𝔽5))⋊D7 |
| commutator, hypocenter | C5×C72 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72 | C2×C4 |
| prime radical | C2×D5×C7⋊D7 | C2 |
| cosocle | C72×D5 | C23 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
312 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#87639, C2×D72×AGL(1,𝔽5), #72243483, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#87639, C2×D72×AGL(1,𝔽5), #72243483, … |
| maximal quotient of | #72243497 |
Past the SmallGroups library coverage — no SmallGroups id.