Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #11765612 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived | C33×C7 ⋊ C2×C3 |
| Hall | #10588048 ⋊ C2 |
| Sylow | C7 ⋊ #4175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C33×C7 | C2×C3 |
| Frattini | C32 | D3×ΓL(1,𝔽8) |
| socle | C3×C7 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C33×C7 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
Polycyclic presentation:
2,3^4,7|c^a=c^2,d^a=d^2,e^a=e^2,c^b=cd,d^b=de,f^b=f^243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 42);