Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C191 ⋊ Q64 |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^1901064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q64×D191, C2×#27132503, #37574827, … |
| maximal normal subgroup of | Q64×D191, C2×#27132503, #37574827, … |
| maximal quotient of | #37570700, #37570701, #37570719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 389);