Finite Group DatabasebetaFinite Group Databasebeta| order | 10550 |
| automorphism | Aut(G) order 22155000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5275 |
| unambiguous semidirect product | C25⋊D211 |
| unambiguous semidirect product | C211⋊D25 |
| Fitting, derived, Hall | C25×C211 ⋊ C2 |
| Sylow | C211 ⋊ D25 |
| Sylow | C25 ⋊ D211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C211 | C2 |
| Frattini | C5 | D1055 |
| socle | C5×C211 | D5 |
| LCS | G ▷ C25×C211 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,211,5|b^5=d^4,b^a=b^4d,c^a=c^210,d^a=d^42639 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D211, C2×D5275, C3×D5275, … |
| maximal normal subgroup of | D25×D211, C2×D5275, C3×D5275, … |
| maximal quotient of | Dic5275, C2×D5275, C3×D5275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10550, 6);