Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #1572 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C32×C4 |
| direct product | #1572 |
| Fitting, socle, derived, Sylow | C34 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C34 | C42 |
| prime radical, cosocle | C3⋊D32 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3496);