Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C191 ⋊ C2 |
| Sylow | C191 ⋊ #520 |
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^d=g^1901934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37581345, #37581349, #37581356, … |
| maximal normal subgroup of | #37581345, #37581349, #37581356, … |
| maximal quotient of | #37574874, #37574875, #37574879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1028);