Finite Group DatabasebetaFinite Group Databasebeta| order | 18020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D265 |
| unambiguous semidirect product | (C5×D17)⋊D53 |
| unambiguous semidirect product | (D17×C53)⋊D5 |
| Fitting, socle, derived, Hall | C5×C17×C53 ⋊ C22 |
| Hall | C17×C53 ⋊ C2×D5 |
| Hall | C5×C53 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×D53 |
| Sylow | C53 ⋊ D5×D17 |
| Sylow | C17 ⋊ C2×D265 |
| Sylow | C5 ⋊ D17×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C53 | C22 |
| LCS | G ▷ C5×C17×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4505 |
1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18020, 42);