Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,d^b=de,e^b=ef,g^c=g^136770 conjugacy classes — view the full character table.
| maximal subgroup of | #31783095, #31783097, #31783100, … |
| maximal normal subgroup of | #31783095, #31783097, #31783100, … |
| maximal quotient of | #31782493, #31782570, D16×Dic137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 978);