Finite Group DatabasebetaFinite Group Databasebeta| order | 37011 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C73×C169 ⋊ C3 |
| Sylow | C169 ⋊ C73⋊C3 |
| Sylow | C73 ⋊ C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C73×C169 | C3 |
| Frattini | C13 | #15667865 |
| socle | C13×C73 | C13⋊C3 |
| LCS | G ▷ C73×C169 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12337 |
Polycyclic presentation:
3,13,73,13|b^13=d,b^a=b^9d,c^a=c^8,d^a=d^94115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37011, 5);