Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#11710730 |
| Fitting, Sylow | C2×#62817 ⋊ C3 |
| derived | #62817 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | #62817 | C2×C3 |
| Frattini | C22 | C2×C22⋊(C22⋊A4) |
| Fitting | C2×#62817 | C3 |
| LCS | G ▷ #62817 | |
| UCS | C1 ◁ C23 | |
15950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 15950 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209831, C2×#72209641, C2×#72209772, … |
| maximal normal subgroup of | C2×#72209831, C2×#72209641, C2×#72209772, … |
| maximal quotient of | D3×#11710730, D5×#11710730, C4×#11710730, … |
Past the SmallGroups library coverage — no SmallGroups id.