Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊((C22⋊C9)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C3⋊((C22⋊C9)⋊C2) |
| unambiguous semidirect product | C3⋊(C3×(C22⋊C9)⋊C2) |
| derived | C3×C22⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C2×C3 |
| Frattini | C3 | C3×C3⋊S4 |
| Fitting, socle | C22×C33 | D3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C3 | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 571);