Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | Aut(G) order 14472192 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2692 |
| 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,e^a=e^672,c^b=cd,e^b=e^6722695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36340421, #36340422, #36340423, … |
| maximal normal subgroup of | #36340421, #36340422, #36340423, … |
| maximal quotient of | #36340402, #36340411, C2×Dic2692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 31);