Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×D764 |
| Fitting | C4×C8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570474, #37570476, C8×#15690272, … |
| maximal normal subgroup of | #37570474, #37570476, C8×#15690272, … |
| maximal quotient of | C8×D1528, C8×#15690276, C8×Dic764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 616);