Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | D7×#737 |
| Fitting, Hall | C7×#737 ⋊ C2 |
| Sylow | C7 ⋊ C2×#737 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C32×D7 |
| commutator, socle, cosocle | C3×C7 | C2×C33 |
| Frattini | C3 | C33×D7 |
| Fitting | C7×#737 | C2 |
| prime radical | D7×H(3,𝔽3) | C3 |
| hypercenter | #737 | D7 |
| hypocenter | C7 | C2×#737 |
| LCS | G ▷ C3×C7 ▷ C7 | |
| UCS | C1 ◁ C9 ◁ #737 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D7×3−1+4, AGL(1,𝔽7)×#737, #72249126, … |
| maximal normal subgroup of | D7×3−1+4, AGL(1,𝔽7)×#737, #72249126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 202);