Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C191 ⋊ C2 |
| Sylow | C191 ⋊ #575 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,e^b=ef,g^d=g^1901067 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37581865, #37581867, #37581874, … |
| maximal normal subgroup of | #37581865, #37581867, #37581874, … |
| maximal quotient of | #37581034, #37581036, #37581107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1345);