Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | D7×#732 |
| Fitting, Hall | C7×#732 ⋊ C2 |
| Sylow | C7 ⋊ C2×#732 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | D7×H(3,𝔽3) |
| commutator, cosocle | C32×C7 | C2×C32 |
| Frattini | C32 | C32×D7 |
| Fitting | C7×#732 | C2 |
| socle | C3×C7 | C2×H(3,𝔽3) |
| hypercenter | #732 | D7 |
| hypocenter | C7 | C2×#732 |
| LCS | G ▷ C32×C7 ▷ C3×C7 ▷ C7 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ #732 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#6911, AGL(1,𝔽7)×#732, #72249148, … |
| maximal normal subgroup of | D7×#6911, AGL(1,𝔽7)×#732, #72249148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 86);