Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C181 ⋊ C2 |
| Sylow | C181 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^180,c^b=cf,d^b=df,g^b=g^1801822 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37533690, #37533692, #37534095, … |
| maximal normal subgroup of | #37533690, #37533692, #37534095, … |
| maximal quotient of | #37532113, #37532139, #37532165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 555);