Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| isoclinism | isoclinic class of #392⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C4×#392⋊C3 |
| Fitting, Sylow | C2×C4×#392 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #127⋊C3 |
| commutator, hypocenter | #95 | C22×C3×C4 |
| Frattini | C24 | C23×A4 |
| Fitting | C2×C4×#392 | C3 |
| socle | C25 | C22×A4 |
| prime radical | C22×#392⋊C3 | C2 |
| cosocle | C2×#95 | C23×C3 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C22×C4 | |
4687 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 4687 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72218286 |
| maximal normal subgroup of | #72218286 |
| maximal quotient of | C2×#72211687, C2×C4×#2017⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.