Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C181 ⋊ #385 |
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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,b^a=bd,c^a=ce,g^a=g^1802908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37534000, #37534001, #37534970, … |
| maximal normal subgroup of | #37534000, #37534001, #37534970, … |
| maximal quotient of | #37531944, #37531954, #37531964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 422);