Finite Group DatabasebetaFinite Group Databasebeta| order | 8714 |
| automorphism | Aut(G) order 18979092 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4357 |
| unambiguous semidirect product | C4357⋊C2 |
| Fitting, socle, derived, Sylow | C4357 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4357 | C2 |
| LCS | G ▷ C4357 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4357|b^a=b^43562180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31775217, C2×D4357, D4357⋊C3, … |
| maximal normal subgroup of | #31775217, C2×D4357, D4357⋊C3, … |
| maximal quotient of | Dic4357, C2×D4357, C3×D4357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8714, 1);