Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C241 ⋊ C4 |
| Sylow | C241 ⋊ #102 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^177,c^b=ce,f^d=f^240314 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21440704, #29508707, #29508708, … |
| maximal normal subgroup of | C2×#21440704, #29508707, #29508708, … |
| maximal quotient of | D4⋊#14515356, #29508565, #29508568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 208);