Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C241 ⋊ C2 |
| 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,c^b=ce,f^b=f^2401214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D241, C2×#21440562, #29507711, … |
| maximal normal subgroup of | #102×D241, C2×#21440562, #29507711, … |
| maximal quotient of | #29507444, #29507450, #29507460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 66);