Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25×C3 |
| direct product | D32×A4⋊S4 |
| Fitting, socle | C24×C32 ⋊ C22×C3⋊D3 |
| derived | C32×A42 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×A42 | C23 |
| Fitting, socle | C24×C32 | C22×C3⋊D3 |
| LCS | G ▷ C32×A42 | |
| UCS | C1 | |
8177 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 8177 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| holomorph of | D3×A4 |
Past the SmallGroups library coverage — no SmallGroups id.