Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C241 ⋊ C4 |
| Sylow | C241 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,b^a=bc,c^a=ce,f^a=f^177,d^b=de,f^d=f^240491 conjugacy classes — view the full character table.
| maximal subgroup of | #29508617, #29508618, #29508619, … |
| maximal normal subgroup of | #29508617, #29508618, #29508619, … |
| maximal quotient of | #29508560, #29508563, #29508568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 204);