Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C27⋊A4 |
| unambiguous semidirect product | (C2×C27)⋊A4 |
| Fitting | C23×C27 ⋊ C3 |
| Sylow | C23 ⋊ C27⋊C3 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic27⋊A4, C4×C27⋊A4, C2×D27⋊A4, … |
| maximal normal subgroup of | Dic27⋊A4, C4×C27⋊A4, C2×D27⋊A4, … |
| maximal quotient of | C4×C27⋊A4, C2×C27⋊SL(2,𝔽3), #13047231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 303);