Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
| direct product | C22×#72224760 |
| Fitting | C22×#63011 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72224760 |
| commutator, cosocle | #3549⋊C3 | C24 |
| Frattini | C23 | C23×#1020 |
| Fitting | C22×#63011 | D3 |
| socle | C24 | #87524 |
| hypocenter | #5464 | C22×D4 |
| LCS | G ▷ #3549⋊C3 ▷ #5464 | |
| UCS | C1 ◁ C22 | |
At least 8669 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has at least 8669 conjugacy classes of subgroups — too many to draw. Only its 218 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 quotient of | #72340866 |
| automorphism group of | #23794, #23795 |
Past the SmallGroups library coverage — no SmallGroups id.