Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C163 ⋊ C2 |
| Sylow | C163 ⋊ #559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D163 |
| commutator, socle, cosocle | C22×C163 | C24 |
| Fitting | C4×Q8×C163 | C2 |
| prime radical | #19104732 | C2 |
| hypercenter | C4×Q8 | D163 |
| hypocenter | C163 | #559 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,163|a^2=f,b^2=ef,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^1621645 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35213594, #35213597, #35213656, … |
| maximal normal subgroup of | #35213594, #35213597, #35213656, … |
| maximal quotient of | #35217491, #35217493, #35217505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 1284);