Finite Group DatabasebetaFinite Group Databasebeta| order | 17980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#10596817 |
| Fitting, socle, derived, Hall | C5×C29×C31 ⋊ C4 |
| Hall | C29×C31 ⋊ Dic5 |
| Hall | C5×C31 ⋊ #1181 |
| Hall | C5×C29 ⋊ Dic31 |
| Sylow | C31 ⋊ #10596817 |
| Sylow | C29 ⋊ Dic155 |
| Sylow | C5 ⋊ C31⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C29×C31 | C4 |
| prime radical, cosocle | C5×C31×D29 | C2 |
| LCS | G ▷ C5×C29×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4495 |
Polycyclic presentation:
2^2,5,29,31|a^2=b,c^a=c^4,d^a=d^17,e^a=e^30,d^b=d^281243 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17980, 34);