Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #456 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^130,d^c=df926 conjugacy classes — view the full character table.
| maximal subgroup of | #30664114, #30664116, #30667982, … |
| maximal normal subgroup of | #30664114, #30664116, #30667982, … |
| maximal quotient of | #30664922, #30664929, #30664934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 731);