Finite Group DatabasebetaFinite Group Databasebeta| order | 8476 |
| automorphism | Aut(G) order 8238672 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4238 |
| direct product | C2×D2119 |
| unambiguous semidirect product | (C2×C13)⋊D163 |
| unambiguous semidirect product | (C2×C163)⋊D13 |
| Fitting, socle | C2×C13×C163 ⋊ C2 |
| derived, Hall | C13×C163 ⋊ C22 |
| Sylow | C163 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D163 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2119 |
| commutator, hypocenter | C13×C163 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C163 | C2 |
| LCS | G ▷ C13×C163 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2122 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27163304, C2×#27163305, C2×(C13⋊C3)⋊D163, … |
| maximal normal subgroup of | C2×#27163304, C2×#27163305, C2×(C13⋊C3)⋊D163, … |
| maximal quotient of | D3×D2119, C2×C3×D2119, C2×D6357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8476, 9);