Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #1088⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#1088⋊C2 |
| unambiguous semidirect product | #1088⋊(C2×C3) |
| unambiguous semidirect product | (((C3⋊D3)⋊C3)⋊C2)⋊(C2×C3) |
| Fitting, Sylow | C3×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #1088⋊C2 |
| commutator, cosocle | #272 | C22×C3 |
| Frattini | C3 | C3×GO+(4,𝔽2) |
| Fitting | C3×H(3,𝔽3) | D4 |
| socle | C32 | GO+(4,𝔽2) |
| hypocenter | H(3,𝔽3) | C3×D4 |
| LCS | G ▷ #272 ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
107 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#6249⋊C2, #13049184, D3×#1088⋊C2, … |
| maximal normal subgroup of | C3×#6249⋊C2, #13049184, D3×#1088⋊C2, … |
| maximal quotient of | C3×#88587, C3×#88588, C3×#88589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 543);