Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#66321 |
| derived | H(3,𝔽3) ⋊ C2×C3×C4 |
| Sylow | AΣL(1,𝔽27) ⋊ C2×C4 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13046480, #13046481, #13046483, … |
| maximal normal subgroup of | #13046480, #13046481, #13046483, … |
| maximal quotient of | C2×#10619500, #13046628, C4×#66321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 158);