Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×Q128 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C71 | D32 |
| commutator, Frattini, cosocle | C32 | C22×C71 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C4×C71 ◁ C8×C71 ◁ C16×C71 ◁ C32×C71 ◁ G | |
36 conjugacy classes of subgroups.
2485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 163);