Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | C2×#11757163⋊C2 |
| Fitting, socle | C25 ⋊ S5 |
| derived | #11757163 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757163⋊C2 |
| commutator, cosocle, hypocenter | #11757163 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C25 | S5 |
| LCS | G ▷ #11757163 | |
| UCS | C1 ◁ C2 | |
953 conjugacy classes of subgroups; only the 9 normal subgroups are shown.
This group has 953 conjugacy classes of subgroups — too many to draw. Only its 9 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
36 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.