Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #328 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^1361379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #328×D137, C2×#22577139, #31779272, … |
| maximal normal subgroup of | #328×D137, C2×#22577139, #31779272, … |
| maximal quotient of | #31778611, #31778614, #31778668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 285);