Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #460 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^130,e^c=ef,g^c=g^1301319 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30665021, #30665022, #30665027, … |
| maximal normal subgroup of | #30665021, #30665022, #30665027, … |
| maximal quotient of | #30665310, #30665322, #30665332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 750);