Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C137 ⋊ C4 |
| Sylow | C137 ⋊ #444 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^100,d^b=df,g^b=g^136,g^c=g^100,g^e=g^136260 conjugacy classes — view the full character table.
| maximal subgroup of | #31797196, #31797197, #31797200, … |
| maximal normal subgroup of | #31797196, #31797197, #31797200, … |
| maximal quotient of | #31796379, #31796382, #31796387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1595);