Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| 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^240,c^b=ce1214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D241, C2×#21440563, #29507710, … |
| maximal normal subgroup of | #102×D241, C2×#21440563, #29507710, … |
| maximal quotient of | D4⋊#14515349, #29507451, #29507461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 67);