Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#72240418 |
| Fitting, Sylow | C2×#72233922 ⋊ C3 |
| derived | #13829 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72240418 |
| commutator, cosocle, hypocenter | #13829 | C23×C3 |
| Frattini | C24 | C23×C22⋊A4 |
| Fitting | C2×#72233922 | C3 |
| socle | C25 | C22×C22⋊A4 |
| LCS | G ▷ #13829 | |
| UCS | C1 ◁ C2 | |
At least 11226 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has at least 11226 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72260915 |
| maximal normal subgroup of | C2×#72260915 |
| maximal quotient of | C2×#72260766 |
Past the SmallGroups library coverage — no SmallGroups id.