Finite Group DatabasebetaFinite Group Databasebeta| order | 10137 |
| isoclinism | isoclinic class of C109⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C109⋊C3 |
| unambiguous semidirect product | C109⋊(C3×C31) |
| Fitting, socle, Hall | C31×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C109 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
1209 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31×C109⋊C3, C31×D109⋊C3, D31×C109⋊C3, … |
| maximal normal subgroup of | C2×C31×C109⋊C3, C31×D109⋊C3, D31×C109⋊C3, … |
| maximal quotient of | C2×C31×C109⋊C3, C31×#11758279, C3×C31×C109⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10137, 2);