Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C163⋊#564 |
| Sylow | C163 ⋊ #564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D163 |
| commutator, socle, prime radical, cosocle | C22×C163 | C24 |
| Fitting | #125×C163 | C2 |
| hypercenter | #125 | D163 |
| hypocenter | C163 | #564 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ #125 | |
172 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,163|a^2=e,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^d=g^1621153 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35213837, #35213839, #35213862, … |
| maximal normal subgroup of | #35213837, #35213839, #35213862, … |
| maximal quotient of | #35217718, #35217719, #35217720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 1304);