Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C109 ⋊ C2 |
| Sylow | C109 ⋊ #453 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^108,d^b=df,e^b=ef,d^c=df934 conjugacy classes — view the full character table.
| maximal subgroup of | #28365014, #28365026, #28365036, … |
| maximal normal subgroup of | #28365014, #28365026, #28365036, … |
| maximal quotient of | #28361950, #28361955, #28361978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 717);