Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#15690287 |
| Fitting | C2×C42×C191 ⋊ C2 |
| Sylow | C191 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 159 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 | #37570900, #37570903, #37570905, … |
| maximal normal subgroup of | #37570900, #37570903, #37570905, … |
| maximal quotient of | C4×#20259281, C4×#20259279, C42×C22⋊D191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1018);