Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C28 |
| direct product | C22×#72209772 |
| Fitting | C22×#62817 ⋊ D3 |
| derived | #11710730 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #11715850 |
| commutator, cosocle, hypocenter | #11710730 | C23 |
| Frattini | C22 | C22×#87588 |
| Fitting | C22×#62817 | D3 |
| hypercenter | C24 | #87588 |
| LCS | G ▷ #11710730 | |
| UCS | C1 ◁ C23 ◁ C24 | |
At least 12062 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has at least 12062 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
132 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72209832 |
| maximal normal subgroup of | C22×#72209832 |
Past the SmallGroups library coverage — no SmallGroups id.