Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C44 |
| direct product | C2×#11709197 |
| Fitting, Sylow | C2×C44 ⋊ C3 |
| derived | C44 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11709197 |
| commutator, cosocle, hypocenter | C44 | C2×C3 |
| Frattini | C24 | C2×C22⋊A4 |
| Fitting | C2×C44 | C3 |
| socle | C25 | C22⋊A4 |
| LCS | G ▷ C44 | |
| UCS | C1 ◁ C2 | |
4612 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209990, #72209996, #72210007, … |
| maximal normal subgroup of | C2×#72209990, #72210007, C2×C42⋊C32, … |
| maximal quotient of | C22×#11709197, C4×#11709197, C2×#72222569, … |
Past the SmallGroups library coverage — no SmallGroups id.