Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #448 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^130,d^b=df1319 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664911, #30664912, #30664922, … |
| maximal normal subgroup of | #30664911, #30664912, #30664922, … |
| maximal quotient of | #30664884, #30664901, #30664952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 688);