Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C181 ⋊ #467 |
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^b=g^1801282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #467×D181, C2×#26041518, #37543297, … |
| maximal normal subgroup of | #467×D181, C2×#26041518, #37543297, … |
| maximal quotient of | #37533084, #37533089, #37533118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 788);