Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C257 · Schur multiplier (H2) = C22 |
| direct product | C2×M16×C257 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C257 | C22 |
| commutator | C2 | C22×C4×C257 |
| Frattini, cosocle | C4 | C23×C257 |
| socle | C22×C257 | C2×C4 |
| prime radical | C23×C257 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C257 ◁ G | |
68 conjugacy classes of subgroups.
5140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 37);