Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #489 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^108,c^b=cf,g^b=g^108,g^c=g^108772 conjugacy classes — view the full character table.
| maximal subgroup of | #28362336, #28362337, #28362346, … |
| maximal normal subgroup of | #28362336, #28362337, #28362346, … |
| maximal quotient of | #28363167, #28363721, #28363728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 911);