Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #486 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^1302102 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30665052, #30665053, #30665059, … |
| maximal normal subgroup of | #30665052, #30665053, #30665059, … |
| maximal quotient of | #30666089, #30666644, #30666767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 896);