Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #88790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#88790 |
| Sylow | C34 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | #6291 |
| commutator, cosocle | C33×C4 | C22×C3 |
| Frattini | C4 | C3×D3×C3⋊D3 |
| Fitting | C34×C4 | C22 |
| socle | C2×C34 | D4 |
| hypercenter | C3×C4 | D3×C3⋊D3 |
| hypocenter | C33 | C3×D8 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
628 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2733);