Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
| direct product | C2×#72240898 |
| Fitting | C2×#7667013 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11715754 |
| commutator, cosocle, hypocenter | #2679⋊C3 | C24 |
| Frattini | C23 | C23×#1020 |
| Fitting | C2×#7667013 | D3 |
| socle | C24 | C22×#1020 |
| LCS | G ▷ #2679⋊C3 | |
| UCS | C1 ◁ C2×C4 | |
40761 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 40761 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240903 |
| maximal normal subgroup of | C2×#72240903 |
Past the SmallGroups library coverage — no SmallGroups id.