Finite Group DatabasebetaFinite Group Databasebeta| order | 837 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊C27 |
| derived, Sylow | C31 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C31⋊C3 |
| commutator, hypocenter | C31 | C27 |
| Fitting, cosocle | C9×C31 | C3 |
| socle, prime radical | C3×C31 | C9 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 837 |
Polycyclic presentation:
3^3,31|a^3=b,b^3=c,d^a=d^25117 conjugacy classes — view the full character table.
| maximal subgroup of | D31⋊C27, C2×C31⋊C27, C27×C31⋊C3, … |
| maximal normal subgroup of | D31⋊C27, C2×C31⋊C27, C27×C31⋊C3, … |
| maximal quotient of | C2×C31⋊C27, C31⋊C81, C3×C31⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(837, 1);