Finite Group DatabasebetaFinite Group Databasebeta| order | 37060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C17×C109 ⋊ C4 |
| Hall | C17×C109 ⋊ AGL(1,𝔽5) |
| Hall | C5×C109 ⋊ #595 |
| Sylow | C109 ⋊ #66775 |
| Hall | C5×C17 ⋊ Dic109 |
| Sylow | C17 ⋊ #14546128 |
| Sylow | C5 ⋊ #20301852 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C109 | C4 |
| prime radical, cosocle | C109×D85 | C2 |
| LCS | G ▷ C5×C17×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9265 |
Polycyclic presentation:
2^2,5,17,109|a^2=b,c^a=c^2,d^a=d^13,e^a=e^108,c^b=c^4,d^b=d^162401 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37060, 24);