Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C191 ⋊ #340 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^1901928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #340×D191, C2×#27132425, #37572235, … |
| maximal normal subgroup of | #340×D191, C2×#27132425, #37572235, … |
| maximal quotient of | #37570354, #37570359, #37570361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 311);