Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C673 ⋊ C2 |
| Sylow | C673 ⋊ SD16 |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^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 | SD16×D673, C2×#24924630, #36340497, … |
| maximal normal subgroup of | SD16×D673, C2×#24924630, #36340497, … |
| maximal quotient of | #36340397, #36340401, #36340408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 27);