Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C257 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,ℤ/8)×C257 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C257 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C23×C257 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C257 ◁ C2×C4×C257 ◁ G | |
68 conjugacy classes of subgroups.
2827 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 43);