Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C257 · Schur multiplier (H2) = C22 |
| direct product | C22⋊Q8×C257 |
| unambiguous semidirect product | C22⋊(Q8×C257) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C257 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C257 |
| prime radical | C23×C257 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C257 ◁ G | |
74 conjugacy classes of subgroups.
3598 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 29);