Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×C22⋊D191 |
| Fitting | C22×Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37584023, #37584024, #37584030, … |
| maximal normal subgroup of | #37584023, #37584024, #37584030, … |
| maximal quotient of | Q8×(C2×D191)⋊C4, Q8×C22⋊Dic191, C4⋊C4×C22⋊D191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1213);