Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10597292 |
| Sylow | C19 ⋊ C2×#103 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10597292, #103×Dic19, #14563465, … |
| maximal normal subgroup of | C4×#10597292, #103×Dic19, #14563465, … |
| maximal quotient of | C2×Q8⋊(C19⋊C8), #14562038, #14562064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 540);