Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66431 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#66431 |
| Fitting | C22×C32×C9 ⋊ C22 |
| derived, Sylow | C32×C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #66431 |
| commutator, cosocle, hypocenter | C32×C9 | C24 |
| Frattini | C3 | C22×#1113 |
| Fitting | C22×C32×C9 | C22 |
| socle | C22×C33 | C2×D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C22 | |
1000 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D32×D9 |
| maximal normal subgroup of | C22×D32×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3039);