Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #430 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^190,c^b=cf1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572741, #37572742, #37572762, … |
| maximal normal subgroup of | #37572741, #37572742, #37572762, … |
| maximal quotient of | #37571272, #37571287, #37571291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 598);