Finite Group DatabasebetaFinite Group Databasebeta| order | 5650 |
| automorphism | Aut(G) order 6328000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2825 |
| unambiguous semidirect product | C25⋊D113 |
| unambiguous semidirect product | C113⋊D25 |
| Fitting, derived, Hall | C25×C113 ⋊ C2 |
| Sylow | C113 ⋊ D25 |
| Sylow | C25 ⋊ D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C113 | C2 |
| Frattini | C5 | D565 |
| socle | C5×C113 | D5 |
| LCS | G ▷ C25×C113 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,113,5|b^5=d^4,b^a=b^4d,c^a=c^112,d^a=d^41414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26015116, #26015117, D25×D113, … |
| maximal normal subgroup of | #26015116, #26015117, D25×D113, … |
| maximal quotient of | Dic2825, C2×D2825, C3×D2825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5650, 4);