Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| isoclinism | isoclinic class of #127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22×#1842⋊C3 |
| Fitting, Sylow | C22×#1842 ⋊ C3 |
| derived | C42 ⋊ C22×C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #127⋊C3 |
| commutator, hypocenter | C42 | C22×C3×C8 |
| Frattini | C22×C4 | C23×A4 |
| Fitting | C22×#1842 | C3 |
| socle | C25 | C4×A4 |
| prime radical | C23×C42⋊C3 | C4 |
| cosocle | C43 | C23×C3 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C22×C4 | |
1740 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 1740 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
160 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72211034, C2×#72211239, C2×C4×#1842⋊C3, … |
| maximal normal subgroup of | C2×C4×#1842⋊C3, #72213894, #72214584, … |
| maximal quotient of | C2×C4×#1842⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.