Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #510 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #31782677, #31782680, #31782740, … |
| maximal normal subgroup of | #31782677, #31782680, #31782740, … |
| maximal quotient of | #31782501, #31782508, #31782578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 989);