Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #66431 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C32×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66431 |
| commutator, hypocenter | C32×C9 | C2×C4 |
| Frattini | C2×C3 | #1113 |
| Fitting, cosocle | C2×C32×C9 | C22 |
| socle | C2×C33 | C2×D3 |
| prime radical | C2×C3×C3⋊D3 | D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
143 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^4|b^2=c,e^3=g,d^a=d^2,f^a=f^2,d^b=d^2,e^b=e^2g^2,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | #13048246, D32⋊Dic9, #13048263, … |
| maximal normal subgroup of | #13048246, D32⋊Dic9, #13048263, … |
| maximal quotient of | #13047736, #13047737, #13047764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 417);