Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×Q8×C137 ⋊ C4 |
| Sylow | C137 ⋊ #410 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=f,b^a=bd,d^a=df,g^a=g^100,e^b=ef,g^b=g^136,g^c=g^136,g^e=g^136362 conjugacy classes — view the full character table.
| maximal subgroup of | #31795891, #31796548, #31796638, … |
| maximal normal subgroup of | #31795891, #31796548, #31796638, … |
| maximal quotient of | #31796023, #31796030, #31796032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1530);