Finite Group DatabasebetaFinite Group Databasebeta| order | 8650 |
| automorphism | Aut(G) order 14878000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4325 |
| unambiguous semidirect product | C25⋊D173 |
| unambiguous semidirect product | C173⋊D25 |
| Fitting, derived, Hall | C25×C173 ⋊ C2 |
| Sylow | C173 ⋊ D25 |
| Sylow | C25 ⋊ D173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C173 | C2 |
| Frattini | C5 | D865 |
| socle | C5×C173 | D5 |
| LCS | G ▷ C25×C173 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,173,5|b^5=d^4,b^a=b^4d,c^a=c^172,d^a=d^42164 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31772402, #31772403, D25×D173, … |
| maximal normal subgroup of | #31772402, #31772403, D25×D173, … |
| maximal quotient of | Dic4325, C2×D4325, C3×D4325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8650, 4);