Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C181 ⋊ C4 |
| Sylow | C181 ⋊ #444 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^162,d^b=df,g^b=g^180,g^c=g^162,g^e=g^180337 conjugacy classes — view the full character table.
| maximal subgroup of | #37550128, #37550129, #37550132, … |
| maximal normal subgroup of | #37550128, #37550129, #37550132, … |
| maximal quotient of | #37549311, #37549314, #37549319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1595);