Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #6295 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#6296 |
| Sylow | C34 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1113 |
| commutator, cosocle | C2×C33 | C22×C3 |
| Frattini | C2 | C3×#1113 |
| Fitting, socle, prime radical | C2×C34 | C22 |
| hypocenter | C33 | C3×Q8 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C3 | |
254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88937, C3×#88938, C3×#88942, … |
| maximal normal subgroup of | C3×#88937, C3×#88938, C3×#88942, … |
| maximal quotient of | C3×#88815, C2×C3×#6296, C3×#10619895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 660);