Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20259341 |
| Fitting | C2×D8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#135 |
266 conjugacy classes of subgroups.
1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574224, #37574229, #37574266, … |
| maximal normal subgroup of | #37574224, #37574229, #37574266, … |
| maximal quotient of | C2×#27132656, C2×#27132700, C2×D8×Dic191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1328);