Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C181 ⋊ C4 |
| Sylow | C181 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^162,c^b=cf,g^e=g^180472 conjugacy classes — view the full character table.
| maximal subgroup of | #37549676, #37549677, #37549680, … |
| maximal normal subgroup of | #37549676, #37549677, #37549680, … |
| maximal quotient of | #37549272, #37549273, #37549274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1560);