Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C191 ⋊ #501 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,c^b=cf,g^b=g^1901346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #501×D191, C2×#27133070, #37583041, … |
| maximal normal subgroup of | #501×D191, C2×#27133070, #37583041, … |
| maximal quotient of | #37572685, #37573256, #37573257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 956);