Finite Group DatabasebetaFinite Group Databasebeta| order | 1674 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C1 |
| direct product | C2×C31⋊C27 |
| unambiguous semidirect product | (C2×C31)⋊C27 |
| derived, Sylow | C31 ⋊ C2×C27 |
| Hall | C2×C31 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C31⋊C3 |
| commutator, hypocenter | C31 | C2×C27 |
| Frattini | C9 | C2×C31⋊C3 |
| Fitting | C2×C9×C31 | C3 |
| socle, prime radical | C2×C3×C31 | C9 |
| cosocle | C9×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C9 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 1674 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1674, 2);