Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
| direct product | C22×D5×#1020 |
| Fitting, socle | C26×C5 ⋊ C2×D3 |
| derived | C5×C22⋊A4 ⋊ C24 |
| Sylow | C5 ⋊ C23×#1020 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×#1020 |
| commutator, cosocle, hypocenter | C5×C22⋊A4 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C26×C5 | C2×D3 |
| LCS | G ▷ C5×C22⋊A4 | |
| UCS | C1 ◁ C22 | |
24164 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 24164 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽5)×#1020, D5×#11713200, #72243698, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#1020, D5×#11713200, #72243698 |
Past the SmallGroups library coverage — no SmallGroups id.