Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D3×3−1+2 |
| unambiguous semidirect product | (C4×D3×C9)⋊C3 |
| Fitting | C3×C4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ C2×C4 |
161 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×3−1+2⋊C8, #88420⋊C3, D3×C8×3−1+2, … |
| maximal normal subgroup of | D3×3−1+2⋊C8, #88420⋊C3, D3×C8×3−1+2, … |
| maximal quotient of | D3×C8×3−1+2, 3−1+2×ΓL(1,𝔽25), C4×Dic3×3−1+2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 455);