Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of #64525 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#64525 |
| Fitting | C22×D4×C19 ⋊ C2 |
| Sylow | C19 ⋊ C22×D8 |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14563980, #14563981, #14563983, … |
| maximal normal subgroup of | #14563980, #14563981, #14563983, … |
| maximal quotient of | C22×#10597266, C22×#10597289, C22×#10597264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1318);