Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#638⋊C3 |
| unambiguous semidirect product | #638⋊C32 |
| unambiguous semidirect product | (C3×#638)⋊C3 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ D4 |
250 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | #89031⋊C3, C3×#88671, #89029⋊C3, … |
| maximal normal subgroup of | #89031⋊C3, C3×#88671, #89029⋊C3, … |
| maximal quotient of | C3×#3750⋊C3, C3×#3752⋊C3, C3×#3754⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 463);