Finite Group DatabasebetaFinite Group Databasebeta| order | 31557 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C67×C157 ⋊ C3 |
| Sylow | C157 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C67×C157 | C3 |
| LCS | G ▷ C67×C157 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10519 |
Polycyclic presentation:
3,67,157|b^a=b^29,c^a=c^123509 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31557, 3);