Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| isoclinism | isoclinic class of #2017⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×#2017⋊C3 |
| Fitting, Sylow | C4×#2017 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #127⋊C3 |
| commutator, hypocenter | #338 | C2×C3×C4 |
| Frattini | C23×C4 | C22×A4 |
| Fitting | C4×#2017 | C3 |
| socle | C22 | C2×#392⋊C3 |
| prime radical | C2×#2017⋊C3 | C2 |
| cosocle | C2×#338 | C22×C3 |
| LCS | G ▷ #338 | |
| UCS | C1 ◁ C42 | |
724 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#2017⋊C3, #72218424 |
| maximal normal subgroup of | C2×C4×#2017⋊C3, #72218424 |
| maximal quotient of | #72211696, C2×C4×#2017⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.