Finite Group DatabasebetaFinite Group Databasebeta| order | 18020 |
| isoclinism | isoclinic class of #66774 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#66774 |
| Fitting, socle, Hall | C5×C17×C53 ⋊ C4 |
| derived, Hall | C5×C17 ⋊ C4×C53 |
| Hall | C17×C53 ⋊ AGL(1,𝔽5) |
| Hall | C5×C53 ⋊ Dic17 |
| Sylow | C17 ⋊ AGL(1,𝔽5)×C53 |
| Sylow | C5 ⋊ C53×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | #66774 |
| commutator, hypocenter | C5×C17 | C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C53 | C4 |
| prime radical | D5×C17×C53 | C2 |
| cosocle | D5×C17 | C2×C53 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4505 |
1961 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18020, 29);