Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×#4169 |
| Fitting | C22×C32⋊C9 ⋊ C2 |
| derived | C3×C9 ⋊ C23×C3 |
| Sylow | C32⋊C9 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #4169 |
| commutator, cosocle, hypocenter | C3×C9 | C23×C3 |
| Frattini | C32 | C22×C3×D3 |
| Fitting | C22×C32⋊C9 | C2 |
| socle | C22×C32 | C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13046469, #13046602, C2×#4169⋊C4, … |
| maximal normal subgroup of | #13046469, #13046602, C2×#4169⋊C4, … |
| maximal quotient of | C2×#10619590, C2×C4×#4169, C2×C4⋊#4169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 323);