Finite Group DatabasebetaFinite Group Databasebeta| order | 651 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C31⋊C3 |
| unambiguous semidirect product | C31⋊(C3×C7) |
| Fitting, socle, Hall | C7×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 217 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D31⋊C3, D7×C31⋊C3, (C31⋊C3)⋊D7, … |
| maximal normal subgroup of | C7×D31⋊C3, D7×C31⋊C3, (C31⋊C3)⋊D7, … |
| maximal quotient of | C2×C7×C31⋊C3, C7×C31⋊C9, C3×C7×C31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(651, 2);