Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C32 |
| direct product | C23×C32×C3⋊D3 |
| Fitting, socle | C23×C34 ⋊ C2 |
| derived | C32 ⋊ C24×C32 |
| Sylow | C34 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C32 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C24×C32 |
| Frattini | C1 | G |
| Fitting, socle | C23×C34 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C32 | |
3820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×C3⋊D32, C2×C32×#3811, C2×C3×C3⋊D3×#67, … |
| maximal normal subgroup of | C23×C3⋊D32, C2×C32×#3811, C2×C3×C3⋊D3×#67, … |
| maximal quotient of | C2×C32×D4×C3⋊D3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3606);