Finite Group DatabasebetaFinite Group Databasebeta| order | 26980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(C71⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C71⋊(C19⋊AGL(1,𝔽5)) |
| Fitting, socle, derived, Hall | C5×C19×C71 ⋊ C4 |
| Hall | C19×C71 ⋊ AGL(1,𝔽5) |
| Hall | C5×C71 ⋊ Dic19 |
| Hall | C5×C19 ⋊ Dic71 |
| Sylow | C71 ⋊ C19⋊AGL(1,𝔽5) |
| Sylow | C19 ⋊ C71⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic1349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C71 | C4 |
| prime radical, cosocle | D5×C19×C71 | C2 |
| LCS | G ▷ C5×C19×C71 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6745 |
Polycyclic presentation:
2^2,5,19,71|a^2=b,c^a=c^2,d^a=d^18,e^a=e^70,c^b=c^42701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26980, 23);