Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C27 |
| direct product | C2×#72227766 |
| Fitting | C2×#8932885 ⋊ D3 |
| derived | #72227294 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C24 | #87588 |
| commutator, cosocle, hypocenter | #72227294 | C22 |
| Frattini | C23 | C2×#87588 |
| Fitting | C2×#8932885 | D3 |
| LCS | G ▷ #72227294 | |
| UCS | C1 ◁ C24 | |
101647 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 101647 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
118 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.