Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C163 ⋊ C2 |
| Sylow | C163 ⋊ #533 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D163 |
| commutator, socle, cosocle | C22×C163 | C24 |
| Fitting | #125×C163 | C2 |
| prime radical | C22×D163 | C23 |
| hypercenter | #125 | D163 |
| hypocenter | C163 | #533 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ #125 | |
222 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,163|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^b=g^162,g^c=g^162,g^d=g^1621162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35213129, #35213149, #35213172, … |
| maximal normal subgroup of | #35213129, #35213149, #35213172, … |
| maximal quotient of | #35216942, #35217009, #35217017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 1105);