Finite Group DatabasebetaFinite Group Databasebeta| order | 567 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C7×3−1+2 ⋊ C3 |
| Sylow | C7 ⋊ #731 |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
3^4,7|b^3=d,b^a=bc,c^a=cd^2,e^a=e^2,c^b=cd39 conjugacy classes — view the full character table.
| maximal subgroup of | #10588045⋊C2, C2×#10588045, ΓL(1,𝔽8)×#731, … |
| maximal normal subgroup of | #10588045⋊C2, C2×#10588045, ΓL(1,𝔽8)×#731, … |
| maximal quotient of | C2×#10588045, #13133436, #13133439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(567, 20);