Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×Dic382 |
| Sylow | C191 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570498, #37570500, C8×#15690275, … |
| maximal normal subgroup of | #37570498, #37570500, C8×#15690275, … |
| maximal quotient of | C8×C4⋊Dic191, C8×Dic191⋊C4, #37573076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 674);