Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C181 ⋊ C2 |
| Sylow | C181 ⋊ #554 |
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^1801285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #554×D181, C2×#26041983, #37547273, … |
| maximal normal subgroup of | #554×D181, C2×#26041983, #37547273, … |
| maximal quotient of | #37536593, #37536595, #37536619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1253);