Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C27 |
| direct product | C2×#72233447 |
| Fitting | C2×#6499874 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72209653 |
| commutator, cosocle, hypocenter | #11710730 | C23 |
| Frattini | C24 | C22×#1020 |
| Fitting | C2×#6499874 | D3 |
| hypercenter | C23 | #87588⋊C2 |
| LCS | G ▷ #11710730 | |
| UCS | C1 ◁ C22 ◁ C23 | |
At least 10703 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has at least 10703 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72233475 |
| maximal normal subgroup of | C2×#72233475 |
Past the SmallGroups library coverage — no SmallGroups id.