Finite Group DatabasebetaFinite Group Databasebeta| order | 6916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D247 |
| unambiguous semidirect product | (C13×D7)⋊D19 |
| unambiguous semidirect product | (D7×C19)⋊D13 |
| Fitting, socle, derived, Hall | C7×C13×C19 ⋊ C22 |
| Hall | C13×C19 ⋊ C2×D7 |
| Hall | C7×C19 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D19 |
| Sylow | C19 ⋊ D7×D13 |
| Sylow | C13 ⋊ D7×D19 |
| Sylow | C7 ⋊ C2×D247 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C19 | C22 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
625 conjugacy classes — view the full character table.
| maximal subgroup of | #35208930, #35208931, #10587720⋊D19, … |
| maximal normal subgroup of | #35208930, #35208931, #10587720⋊D19, … |
| maximal quotient of | C3×D7×D247, D21×D247, D7×D741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6916, 19);