Finite Group DatabasebetaFinite Group Databasebeta| order | 17980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#10596814 |
| Fitting, socle, derived, Hall | C5×C29×C31 ⋊ C4 |
| Hall | C29×C31 ⋊ AGL(1,𝔽5) |
| Hall | C5×C31 ⋊ #1181 |
| Hall | C5×C29 ⋊ Dic31 |
| Sylow | C31 ⋊ #10596814 |
| Sylow | C29 ⋊ C31⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C31⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C29×C31 | C4 |
| prime radical, cosocle | C31×D145 | 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^2,d^a=d^17,e^a=e^30,c^b=c^4,d^b=d^281150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17980, 27);