Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #10588065⋊C2 |
| Fitting | C7×3−1+2 ⋊ C2×C3 |
| Hall | #10588065 ⋊ C2 |
| Hall | D7 ⋊ #737 |
| Sylow | C7 ⋊ C2×#737 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
2,3^4,7|c^3=e,f^a=f^6,d^b=de,f^b=f^4,d^c=de77 conjugacy classes — view the full character table.
| maximal subgroup of | #72249113, AGL(1,𝔽7)×#737, #72249126, … |
| maximal normal subgroup of | #72249113, AGL(1,𝔽7)×#737, #72249126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 144);