Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #536 |
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^190,c^b=ce1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37573039, #37573055, #37573057, … |
| maximal normal subgroup of | #37573039, #37573055, #37573057, … |
| maximal quotient of | #37575106, #37575113, #37575144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1123);