Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C191 ⋊ C2 |
| Sylow | C191 ⋊ #444 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^190,g^c=g^1901352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574410, #37574414, #37574417, … |
| maximal normal subgroup of | #37574410, #37574414, #37574417, … |
| maximal quotient of | #37571331, #37571338, #37571343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 670);