Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×#4169 |
| Fitting | C23×C32⋊C9 ⋊ C2 |
| derived | C3×C9 ⋊ C24×C3 |
| Sylow | C32⋊C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #4169 |
| commutator, cosocle, hypocenter | C3×C9 | C24×C3 |
| Frattini | C32 | C23×C3×D3 |
| Fitting | C23×C32⋊C9 | C2 |
| socle | C23×C32 | C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C23 | |
1069 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1069 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#4169, C23×#92299, C23×#4169⋊C3 |
| maximal normal subgroup of | C2×D4×#4169, C23×#4169⋊C3 |
| maximal quotient of | C2×D4×#4169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1903);