Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #350 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^127,c^b=cf,d^b=df,g^d=g^100,g^e=g^136113 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22578503, #31797969, #31797971, … |
| maximal normal subgroup of | C2×#22578503, #31797969, #31797971, … |
| maximal quotient of | #31797812, #31797824, D4⋊#14555522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1649);