Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q16×C109 ⋊ C2 |
| Sylow | C109 ⋊ #495 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|b^2=d,c^2=ef,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^108,g^b=g^108,g^c=g^108778 conjugacy classes — view the full character table.
| maximal subgroup of | #28365089, #28365090, #28365096, … |
| maximal normal subgroup of | #28365089, #28365090, #28365096, … |
| maximal quotient of | #28362625, #28362626, #28362635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 934);