Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C181 ⋊ #431 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^162,g^b=g^180,g^e=g^180760 conjugacy classes — view the full character table.
| maximal subgroup of | #37548544, #37548546, #37548606, … |
| maximal normal subgroup of | #37548544, #37548546, #37548606, … |
| maximal quotient of | #37549435, C4×#19153873, C4×#19153883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1567);