Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#20259313 |
| Sylow | C191 ⋊ C2×#125 |
226 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37573474, #37573476, #37573483, … |
| maximal normal subgroup of | #37573474, #37573476, #37573483, … |
| maximal quotient of | C2×#27132528, C2×#27132546, C2×#27132550, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1070);