Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C181 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,181|a^2=e,c^2=e,e^2=f,b^a=bd,g^a=g^19,g^c=g^162,g^e=g^180490 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#26042306, D4×D181⋊C8, #37550435, … |
| maximal normal subgroup of | C2×#26042306, D4×D181⋊C8, #37550435, … |
| maximal quotient of | #37549301, #37549304, #37549305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1576);