Finite Group DatabasebetaFinite Group Databasebeta| order | 8307 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C13⋊C9 |
| unambiguous semidirect product | C13⋊(C9×C71) |
| unambiguous semidirect product | (C13×C71)⋊C9 |
| derived, Sylow | C13 ⋊ C9×C71 |
| Hall | C13×C71 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C71 | C13⋊C3 |
| commutator, hypocenter | C13 | C9×C71 |
| Frattini | C3 | C13⋊C3×C71 |
| Fitting, socle | C3×C13×C71 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C71 | |
12 conjugacy classes of subgroups.
1491 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C71×C13⋊C9, C13⋊C9×D71, C71×D13⋊C9, … |
| maximal normal subgroup of | C2×C71×C13⋊C9, C13⋊C9×D71, C71×D13⋊C9, … |
| maximal quotient of | C2×C71×C13⋊C9, C71×C22⋊(C13⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8307, 2);