Finite Group DatabasebetaFinite Group Databasebeta| order | 10137 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C109 ⋊ C3 |
| Sylow | C109 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C109 | C3 |
| LCS | G ▷ C31×C109 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,31,109|b^a=b^25,c^a=c^451129 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#23778336, #35202478, #35202482, … |
| maximal normal subgroup of | C2×#23778336, #35202478, #35202482, … |
| maximal quotient of | C2×#23778336, #44477326, C3×#23778336 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10137, 4);