Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊(C3⋊#157) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C3⋊(C3⋊#622) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊#622) |
| derived, Sylow | C34 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(C3⋊#157) |
| commutator, hypocenter | C34 | C2×C8 |
| Frattini | C2 | C2×C3⋊(C3⋊#157) |
| Fitting, socle, prime radical | C22×C34 | C4 |
| cosocle | C32×C3⋊Dic3 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13049399, #72252792, #72252871, … |
| maximal normal subgroup of | C2×#13049399, #72252792, #72252871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3312);