Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C191 ⋊ #358 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=f,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^190,c^b=ce,e^b=ef1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #358×D191, C2×#27132467, #37574226, … |
| maximal normal subgroup of | #358×D191, C2×#27132467, #37574226, … |
| maximal quotient of | #37570484, #37570532, #37570569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 353);