Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C181 ⋊ C4 |
| Sylow | C181 ⋊ #389 |
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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=f,b^2=f,c^2=e,b^a=bd,c^a=ce,g^a=g^19,g^b=g^162,g^f=g^180478 conjugacy classes — view the full character table.
| maximal subgroup of | #37549684, #37549685, #37549686, … |
| maximal normal subgroup of | #37549684, #37549685, #37549686, … |
| maximal quotient of | #37548898, #37548901, #37548906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1500);