Finite Group DatabasebetaFinite Group Databasebeta| order | 5584 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C349 · Schur multiplier (H2) = C1 |
| direct product | Q16×C349 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C349 | D4 |
| commutator, Frattini, cosocle | C4 | C22×C349 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C349 ◁ C4×C349 ◁ G | |
18 conjugacy classes of subgroups.
2443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5584, 9);