Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#20259316 |
| Fitting | C2×C42×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#126 |
246 conjugacy classes of subgroups.
3068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570887, #37570890, #37575068, … |
| maximal normal subgroup of | #37570887, #37570890, #37575068, … |
| maximal quotient of | C2×#27132531, C2×#27132547, C2×#27132554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1074);