Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C131 ⋊ #330 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=e,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 | #330×D131, C2×#22553054, #30664548, … |
| maximal normal subgroup of | #330×D131, C2×#22553054, #30664548, … |
| maximal quotient of | #30663784, #30663842, C2×#22553054 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 291);