Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C181 ⋊ C4 |
| Sylow | C181 ⋊ #357 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^162,c^b=ce,e^b=ef,g^d=g^180337 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#26042191, #37550028, #37550029, … |
| maximal normal subgroup of | C2×#26042191, #37550028, #37550029, … |
| maximal quotient of | #37548675, #37548676, #37548707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1461);