Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C109 ⋊ #365 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^108,d^b=df,g^b=g^108772 conjugacy classes — view the full character table.
| maximal subgroup of | #365×D109, C2×#20294850, #28364803, … |
| maximal normal subgroup of | #365×D109, C2×#20294850, #28364803, … |
| maximal quotient of | #28361097, #28361132, C2×#20294850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 373);