Finite Group DatabasebetaFinite Group Databasebeta| order | 37479 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C13×C961 ⋊ C3 |
| Sylow | C961 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C961⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C961 | C3 |
| Frattini | C31 | #11925882 |
| socle | C13×C31 | C31⋊C3 |
| LCS | G ▷ C13×C961 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12493 |
Polycyclic presentation:
3,13,31^2|c^31=d^20,b^a=b^9,c^a=c^5d,d^a=d^54167 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37479, 5);