Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C44 |
| direct product | C2×#13829⋊C3 |
| Fitting, Sylow | C2×#13829 ⋊ C3 |
| derived | #13829 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13829⋊C3 |
| commutator, cosocle, hypocenter | #13829 | C2×C3 |
| Frattini | C24 | C2×C22⋊A4 |
| Fitting | C2×#13829 | C3 |
| socle | C25 | C22⋊A4 |
| LCS | G ▷ #13829 | |
| UCS | C1 ◁ C2 | |
1452 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 1452 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240345, C2×#72240416, C2×#72260904 |
| maximal normal subgroup of | C2×#72240345, C2×#72240416, C2×#72260904 |
| maximal quotient of | C2×#72240347 |
Past the SmallGroups library coverage — no SmallGroups id.