Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C257 · Schur multiplier (H2) = C2 |
| direct product | #106×C257 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C257 | D4 |
| commutator | C4 | C2×C4×C257 |
| Frattini, cosocle | C2×C4 | C22×C257 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C257 ◁ C2×C4×C257 ◁ G | |
36 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, 13);