Finite Group DatabasebetaFinite Group Databasebeta| order | 19670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D281⋊C5) |
| unambiguous semidirect product | (C281⋊C5)⋊D7 |
| unambiguous semidirect product | D1967⋊C5 |
| Fitting, socle, derived, Hall | C7×C281 ⋊ C2×C5 |
| Hall | C7×C281⋊C5 ⋊ C2 |
| Hall | D1967 ⋊ C5 |
| Hall | C281⋊C5 ⋊ D7 |
| Sylow | C281 ⋊ C5×D7 |
| Sylow | C7 ⋊ D281⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C281 | C2×C5 |
| LCS | G ▷ C7×C281 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1967 |
Polycyclic presentation:
2,5,7,281|c^a=c^6,d^a=d^280,d^b=d^86221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19670, 17);