Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20259353 |
| Fitting | C22×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37572886, #37572892, #37572990, … |
| maximal normal subgroup of | #37572886, #37572892, #37572990, … |
| maximal quotient of | C2×#27132672, C2×#27132662, C2×#27132703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1342);