Finite Group DatabasebetaFinite Group Databasebeta| order | 8449 |
| isoclinism | isoclinic class of C71⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C71⋊C7 |
| unambiguous semidirect product | C71⋊(C7×C17) |
| unambiguous semidirect product | (C17×C71)⋊C7 |
| Fitting, socle, Hall | C17×C71 ⋊ C7 |
| derived, Sylow | C71 ⋊ C7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C71⋊C7 |
| commutator, hypocenter | C71 | C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C71 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
289 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C17×C71⋊C7, C17×D71⋊C7, D17×C71⋊C7, … |
| maximal normal subgroup of | C2×C17×C71⋊C7, C17×D71⋊C7, D17×C71⋊C7, … |
| maximal quotient of | C2×C17×C71⋊C7, C3×C17×C71⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8449, 1);