Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×D3×C3⋊(C3⋊D3) |
| Fitting, socle | C2×C34 ⋊ C22 |
| derived, Sylow | C34 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C34 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
1286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6289, D3×#6292, #13049496, … |
| maximal normal subgroup of | D3×#6289, D3×#6292, #13049496, … |
| maximal quotient of | Dic6×C3⋊(C3⋊D3), #13049660, #13049661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 749);