Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C109 ⋊ C2 |
| Sylow | C109 ⋊ #509 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^108,d^b=de,e^b=ef,g^b=g^1081096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28364929, #28364932, #28364979, … |
| maximal normal subgroup of | #28364929, #28364932, #28364979, … |
| maximal quotient of | #28364745, #28364749, #28364820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 987);