Finite Group DatabasebetaFinite Group Databasebeta| order | 10731 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C3×C72) |
| Fitting, socle, Hall | C72×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
1323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×D73⋊C3, C7×(C73⋊C3)⋊D7, C7×D7×C73⋊C3, … |
| maximal normal subgroup of | C72×D73⋊C3, C7×(C73⋊C3)⋊D7, C7×D7×C73⋊C3, … |
| maximal quotient of | C2×C72×C73⋊C3, C72×#10620321, C3×C72×C73⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10731, 15);