Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| isoclinism | isoclinic class of D163 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D163 |
| unambiguous semidirect product | C163⋊C26 |
| unambiguous semidirect product | (C2×C163)⋊C25 |
| Fitting, socle | C25×C163 ⋊ C2 |
| derived, Sylow | C163 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D163 |
| commutator, cosocle, hypocenter | C163 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C163 | C2 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
2656 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #379×D163, C2×#23781520, #35222812, … |
| maximal normal subgroup of | #379×D163, C2×#23781520, #35222812, … |
| maximal quotient of | C24×C4×D163, C25×Dic163, C23×D4×D163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 1387);