Finite Group DatabasebetaFinite Group Databasebeta| order | 9940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic355 |
| derived, Hall | C5×C71 ⋊ C4×C7 |
| Hall | C5×C7×C71 ⋊ C4 |
| Hall | C7×C71 ⋊ Dic5 |
| Sylow | C71 ⋊ C7×Dic5 |
| Hall | C5×C7 ⋊ Dic71 |
| Sylow | C5 ⋊ C7×Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D355 |
| commutator, hypocenter | C5×C71 | C4×C7 |
| Frattini | C2 | C7×D355 |
| Fitting, socle, prime radical | C2×C5×C7×C71 | C2 |
| cosocle | C2×C5×C71 | C2×C7 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
2506 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic355, C7×Dic1065, ΓL(1,𝔽8)×Dic355 |
| maximal normal subgroup of | C3×C7×Dic355, ΓL(1,𝔽8)×Dic355 |
| maximal quotient of | C3×C7×Dic355, C7×Dic1065 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9940, 9);