Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #424 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^190,c^b=cf,g^b=g^1901928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570472, #37572792, #37572793, … |
| maximal normal subgroup of | #37570472, #37572792, #37572793, … |
| maximal quotient of | #37571292, #37571296, #37571301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 577);