Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #448 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^190,d^b=df,g^b=g^1901919 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571473, #37571474, #37571485, … |
| maximal normal subgroup of | #37571473, #37571474, #37571485, … |
| maximal quotient of | #37571445, #37571462, #37571513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 690);