Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C22×Q32×C59 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | D8 |
| commutator, Frattini, cosocle | C8 | C24×C59 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C22×C4×C59 ◁ C22×C8×C59 ◁ G | |
360 conjugacy classes of subgroups.
2596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2142);