Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C109 ⋊ #359 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^33,c^b=ce,e^b=ef,g^b=g^108,g^d=g^108211 conjugacy classes — view the full character table.
| maximal subgroup of | D109⋊#359, C2×#20295941, #28379346, … |
| maximal normal subgroup of | D109⋊#359, C2×#20295941, #28379346, … |
| maximal quotient of | #28377987, #28377988, #28378023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1464);