Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C7×C27 ⋊ C2×C3 |
| Hall | #10588029 ⋊ C2 |
| Hall | D7 ⋊ C27⋊C3 |
| Sylow | C7 ⋊ C2×C27⋊C3 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
2,3^4,7|c^3=d,d^3=e,f^a=f^6,c^b=ce,f^b=f^293 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×C27⋊C3, #72249081 |
| maximal normal subgroup of | AGL(1,𝔽7)×C27⋊C3, #72249081 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 8);