Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D32⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D32⋊D9 |
| Fitting | C2×C32×C9 ⋊ D4 |
| Sylow | C32×C9 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D32⋊D9 |
| commutator, cosocle | C9×C3⋊D3 | C23 |
| Frattini | C3 | C2×D32⋊D3 |
| Fitting | C2×C32×C9 | D4 |
| socle | C2×C33 | #67 |
| hypocenter | C32×C9 | C2×D4 |
| LCS | G ▷ C9×C3⋊D3 ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
298 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2974);