Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊Dic191 |
| Sylow | C191 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570742, #37570743, #37570757, … |
| maximal normal subgroup of | #37570742, #37570743, #37570757, … |
| maximal quotient of | C22×C191⋊#95, C2×C4×C22⋊Dic191, C2×#27132519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 997);