Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C673 ⋊ Q16 |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^6721687 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D673, C2×#24924633, #36340497, … |
| maximal normal subgroup of | Q16×D673, C2×#24924633, #36340497, … |
| maximal quotient of | #36340400, #36340401, #36340410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 30);