Finite Group DatabasebetaFinite Group Databasebeta| order | 9872 |
| automorphism | Aut(G) order 12162304 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2468 |
| Sylow | C617 ⋊ Q16 |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,617|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^616,c^b=cd,e^b=e^6162471 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34089646, #34089647, #34089648, … |
| maximal normal subgroup of | #34089646, #34089647, #34089648, … |
| maximal quotient of | #34089627, #34089636, C2×Dic2468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9872, 31);