Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=f,c^2=ef,d^2=f,b^a=bd,d^a=df,d^b=df,g^c=g^136980 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q16×D137, C2×#22577495, #31789557, … |
| maximal normal subgroup of | C4×Q16×D137, C2×#22577495, #31789557, … |
| maximal quotient of | #31779593, #31779636, #31779642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 641);