Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#20259266 |
| Sylow | C191 ⋊ C2×SD32 |
90 conjugacy classes of subgroups.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#20259266, #37574375, #37574381, … |
| maximal normal subgroup of | C4×#20259266, #37574375, #37574381, … |
| maximal quotient of | C2×#27132464, C2×#27132466, C2×#27132490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 973);