Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #478 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^108,e^c=ef,g^c=g^1081099 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #478×D109, C2×#20295327, #28372819, … |
| maximal normal subgroup of | #478×D109, C2×#20295327, #28372819, … |
| maximal quotient of | #28363043, #28363282, #28363296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 850);