Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C23×C9 ⋊ ΓL(1,𝔽8) |
| Hall | AGL(1,𝔽8) ⋊ 3−1+2 |
| Sylow | C23 ⋊ #4428 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
3^3,7,2^3|b^3=c^2,b^a=bc,d^a=d^2,e^a=ef,f^a=eg,e^d=ef,f^d=g,g^d=e40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 440);