Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4207 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×#4207 |
| Fitting | C22×#737 ⋊ C2 |
| derived | C3×C9 ⋊ C23×C3 |
| Sylow | #737 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #4207 |
| commutator, cosocle, hypocenter | C3×C9 | C23×C3 |
| Frattini | C3 | C22×C3×C3⋊D3 |
| Fitting | C22×#737 | C2 |
| socle | C22×C3 | C3×C3⋊D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22 | |
285 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13047777, #13047960, C2×#4207⋊C4, … |
| maximal normal subgroup of | #13047777, #13047960, C2×#4207⋊C4, … |
| maximal quotient of | C2×#10619965, C2×C4×#4207, C2×C4⋊#4207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 633);