Finite Group DatabasebetaFinite Group Databasebeta| order | 17420 |
| isoclinism | isoclinic class of #63120 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#63120 |
| Fitting, socle, Hall | C5×C13×C67 ⋊ C4 |
| derived, Hall | C5×C13 ⋊ C4×C67 |
| Hall | C13×C67 ⋊ AGL(1,𝔽5) |
| Hall | C5×C67 ⋊ Dic13 |
| Sylow | C13 ⋊ AGL(1,𝔽5)×C67 |
| Sylow | C5 ⋊ Dic13×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #63120 |
| commutator, hypocenter | C5×C13 | C4×C67 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C67 | C4 |
| prime radical | D5×C13×C67 | C2 |
| cosocle | D5×C13 | C2×C67 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C67 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4355 |
1943 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17420, 19);