Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4179 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#66326 |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | #732 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #4179 |
| commutator, hypocenter | C3×C9 | C2×C3×C4 |
| Frattini | C2×C32 | C2×C3×D3 |
| Fitting, prime radical | C22×#732 | C2 |
| socle | C22×C3 | (C3⋊D3)⋊C3 |
| cosocle | C2×C3×C9 | C22×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22 | |
95 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #13046494, #13046495, #13046496, … |
| maximal normal subgroup of | #13046494, #13046495, #13046496, … |
| maximal quotient of | C2×#10619505, #13046654, C4×#66326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 167);