Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| isoclinism | isoclinic class of C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C212 |
| direct product | C23×C22⋊(C22⋊A4) |
| Fitting, socle, Sylow | C29 ⋊ C3 |
| derived | C26 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C26 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C29 | C3 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C23 | |
2762326 conjugacy classes of subgroups; only the 720 normal subgroups are shown.
This group has 2762326 conjugacy classes of subgroups — too many to draw. Only its 720 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
192 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.