Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #11765745 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived | C3×C7×C9 ⋊ C2×C3 |
| Hall | #10588061 ⋊ C2 |
| Sylow | C7 ⋊ #4207 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C9 | C2×C3 |
| Frattini | C3 | C3⋊D3×ΓL(1,𝔽8) |
| socle | C3×C7 | C3×C3⋊D3 |
| LCS | G ▷ C3×C7×C9 | |
| UCS | C1 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
2,3^3,7,3|c^3=f,c^a=c^2f^2,d^a=d^2,f^a=f^2,d^b=df^2,e^b=e^451 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#4207, #72249172, #72249173, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#4207, #72249172, #72249173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 175);