Finite Group DatabasebetaFinite Group Databasebeta| order | 10731 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13095275 |
| Fitting, socle, Hall | C72×C73 ⋊ C3 |
| derived | C7×C73 ⋊ C3×C7 |
| Sylow | C73 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13095275 |
| commutator, cosocle, hypocenter | C7×C73 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C73 | C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
1211 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#15690441, C7×#15690449, C7×#15690445, … |
| maximal normal subgroup of | C7×#15690441, C7×#15690449, C7×#15690445, … |
| maximal quotient of | C2×C7×#13095275, C7×#17987159, C3×C7×#13095275 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10731, 9);