Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C22×#87519 |
| Fitting | C22×#585 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #1020 |
| commutator, cosocle, hypocenter | #997 | C24 |
| Frattini | C2 | C23×#1020 |
| Fitting | C22×#585 | D3 |
| socle | C23 | C2×#1020 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C22×C4 | |
13824 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 13824 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
104 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.