Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#20259279 |
| Fitting | C2×C42×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570832, #37570852, #37572215, … |
| maximal normal subgroup of | #37570832, #37570852, #37572215, … |
| maximal quotient of | C2×#27132509, C2×C4×(C2×D191)⋊C4, C2×C4×Dic191⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1003);