Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C131 ⋊ #329 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^130,c^b=cf,d^b=def929 conjugacy classes — view the full character table.
| maximal subgroup of | #30664108, #30664109, #30664111, … |
| maximal normal subgroup of | #30664108, #30664109, #30664111, … |
| maximal quotient of | #30663782, #30663787, #30663842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 289);