Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C109 ⋊ C4 |
| Sylow | C109 ⋊ #342 |
142 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 36 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=d,b^2=e,b^a=bc,c^a=cf,d^b=df,g^b=g^33,g^e=g^108292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20295903, #28378730, #99×#89137, … |
| maximal normal subgroup of | C2×#20295903, #28378730, #99×#89137, … |
| maximal quotient of | #28377869, #28377873, #28377875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1426);