Finite Group DatabasebetaFinite Group Databasebeta| order | 9940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C71⋊C7)⋊Dic5 |
| unambiguous semidirect product | Dic355⋊C7 |
| derived, Hall | C5×C71 ⋊ C4×C7 |
| Hall | C5×C71⋊C7 ⋊ C4 |
| Hall | Dic355 ⋊ C7 |
| Hall | C71⋊C7 ⋊ Dic5 |
| Sylow | C71 ⋊ C7×Dic5 |
| Sylow | C5 ⋊ Dic71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D71⋊C7) |
| commutator, hypocenter | C5×C71 | C4×C7 |
| Fitting, socle, cosocle | C2×C5×C71 | C2×C7 |
| prime radical | C2×C5×C71⋊C7 | C2 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,71,2|a^2=e,b^a=b^4,d^a=d^70,d^c=d^45106 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C71⋊C7)⋊Dic5, C3⋊((C71⋊C7)⋊Dic5) |
| maximal normal subgroup of | C3×(C71⋊C7)⋊Dic5 |
| maximal quotient of | C3×(C71⋊C7)⋊Dic5, C3⋊((C71⋊C7)⋊Dic5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9940, 14);