Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #10620215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C34 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C34 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
474 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12 |
Polycyclic presentation:
2^3,3^4|d^a=d^2,g^a=g^2,d^b=d^2,f^b=f^2,d^c=d^2,e^c=e^242 conjugacy classes — view the full character table.
| maximal subgroup of | #13049779, (D32⋊D3)⋊D3, (#157⋊D3)⋊D3, … |
| maximal normal subgroup of | #13049779, (D32⋊D3)⋊D3, (#157⋊D3)⋊D3, … |
| maximal quotient of | #13049545, #13049546, #13049547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 734);