Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C22×C3⋊(C3⋊D9) |
| Fitting | C22×C32×C9 ⋊ C2 |
| derived, Sylow | C32×C9 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(C3⋊D9) |
| commutator, cosocle, hypocenter | C32×C9 | C23 |
| Frattini | C3 | C22×C3⋊(C3⋊D3) |
| Fitting | C22×C32×C9 | C2 |
| socle | C22×C33 | D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C22 | |
800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #13047713, #13047714, #13048012, … |
| maximal normal subgroup of | #13047713, #13047714, #13048012, … |
| maximal quotient of | C2×#10619985, C2×C4×C3⋊(C3⋊D9), C2×C4⋊(C3⋊(C3⋊D9)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 635);