Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q8×C109 ⋊ C4 |
| Sylow | C109 ⋊ #419 |
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,109|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^33,c^b=cf,d^b=df,g^e=g^108292 conjugacy classes — view the full character table.
| maximal subgroup of | #28378884, #28378885, #28379031, … |
| maximal normal subgroup of | #28378884, #28378885, #28379031, … |
| maximal quotient of | #28378334, #28378335, #28378336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1542);