Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×C22⋊D191 |
| Fitting | C23×C4×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570836, #37570856, C4×#20259236, … |
| maximal normal subgroup of | #37570836, #37570856, C4×#20259236, … |
| maximal quotient of | C2×C4×C22⋊Dic191, C2×C4×(C2×D191)⋊C4, C2×C4×Dic191⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1008);