Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#72214078 |
| Fitting, Sylow | C2×#72213929 ⋊ C3 |
| derived | C44 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72214078 |
| commutator, cosocle, hypocenter | C44 | C23×C3 |
| Frattini | C24 | C23×C22⋊A4 |
| Fitting | C2×#72213929 | C3 |
| socle | C25 | C22×C22⋊A4 |
| LCS | G ▷ C44 | |
| UCS | C1 ◁ C2 | |
55916 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 55916 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
104 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.