Finite Group DatabasebetaFinite Group Databasebeta| order | 17420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊#63121 |
| Fitting, socle, derived, Hall | C5×C13×C67 ⋊ C4 |
| Hall | C13×C67 ⋊ AGL(1,𝔽5) |
| Hall | C5×C67 ⋊ #261 |
| Sylow | C67 ⋊ #63121 |
| Hall | C5×C13 ⋊ Dic67 |
| Sylow | C13 ⋊ C67⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C67⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C67 | C4 |
| prime radical, cosocle | C67×D65 | C2 |
| LCS | G ▷ C5×C13×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4355 |
Polycyclic presentation:
2^2,5,13,67|a^2=b,c^a=c^2,d^a=d^8,e^a=e^66,c^b=c^4,d^b=d^121142 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17420, 18);