Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C32 |
| direct product | C32×#634 |
| Sylow | C34 ⋊ Q8 |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#3716, C32×#3719, C3×#88792, … |
| maximal normal subgroup of | C32×#3716, C32×#3719, C3×#88792, … |
| maximal quotient of | C32×#3750, C32×C4⋊(C3⋊Dic3), C2×C32×#634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 684);