Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C163 ⋊ #563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D163 |
| commutator, socle, cosocle | C22×C163 | C24 |
| Fitting | #123×C163 | C2 |
| prime radical | C2×D4×C163 | C22 |
| hypercenter | #123 | D163 |
| hypocenter | C163 | #563 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ #123 | |
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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=e,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,g^a=g^162,c^b=cef,d^b=de1153 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35216547, #35216550, #563×D163, … |
| maximal normal subgroup of | #35216547, #35216550, #563×D163, … |
| maximal quotient of | #35217679, #35217684, #35217703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 1302);