Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D191 |
| Fitting | C4⋊Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #332×D191, #333×D191, #37571190, … |
| maximal normal subgroup of | #332×D191, #333×D191, #37571190, … |
| maximal quotient of | #384×D191, #389×D191, #391×D191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1090);