Finite Group DatabasebetaFinite Group Databasebeta| order | 37105 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C181 ⋊ C5 |
| Sylow | C181 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ C181⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C181 | C5 |
| LCS | G ▷ C41×C181 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7421 |
Polycyclic presentation:
5,41,181|b^a=b^37,c^a=c^421489 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37105, 6);