Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#41×C191 ⋊ C2 |
| Sylow | C191 ⋊ #449 |
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^190,d^b=df1919 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #449×D191, C2×#27132808, #37581738, … |
| maximal normal subgroup of | #449×D191, C2×#27132808, #37581738, … |
| maximal quotient of | #37571449, #37571466, #37571517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 694);