Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4207 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×#4207 |
| Fitting | C4×#737 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | #737 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #4207 |
| commutator, hypocenter | C3×C9 | C2×C3×C4 |
| Frattini, socle | C2×C3 | C2×C3×C3⋊D3 |
| Fitting | C4×#737 | C2 |
| prime radical | C2×#4207 | C2 |
| cosocle | C2×C3×C9 | C22×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C4 | |
147 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #4207⋊C8, #13047754, C8×#4207, … |
| maximal normal subgroup of | #4207⋊C8, #13047754, C8×#4207, … |
| maximal quotient of | C8×#4207, #13047912, C4×#66409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 486);