Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C32×D32 |
| unambiguous semidirect product | (C3×D3)⋊(C23×C32) |
| Fitting, socle | C22×C34 ⋊ C22 |
| derived | C32 ⋊ C24×C32 |
| Sylow | C34 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D32 |
| commutator, cosocle, hypocenter | C32 | C24×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C32 | |
2356 conjugacy classes of subgroups; only the 624 normal subgroups are shown.
This group has 2356 conjugacy classes of subgroups — too many to draw. Only its 624 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3597);