Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #10588042 ⋊ C2 |
| Sylow | C7 ⋊ #4178 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #67369 |
| commutator, Fitting, cosocle, hypocenter | C7×H(3,𝔽3) | C2×C3 |
| Frattini | C32 | C3⋊AGL(1,𝔽7) |
| socle | C3×C7 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C7×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
2,3^3,7,3|b^3=f,c^a=c^2,d^a=d^2f,e^a=e^6,c^b=cd,e^b=e^2,d^c=df33 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 54);