Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C181 ⋊ C2 |
| Sylow | C181 ⋊ #575 |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,181|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,g^a=g^180,e^b=ef,g^b=g^1801822 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37534082, #37534084, #37534221, … |
| maximal normal subgroup of | #37534082, #37534084, #37534221, … |
| maximal quotient of | #37542241, #37542311, #37542523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1349);