Finite Group DatabasebetaFinite Group Databasebeta| order | 8992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C281 ⋊ C2 |
| Sylow | C281 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,281|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^280,d^b=de1411 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31823629, #31823630, #31823634, … |
| maximal normal subgroup of | #31823629, #31823630, #31823634, … |
| maximal quotient of | #31823462, #31823468, #31823503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8992, 172);