Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×Dic19 |
| Sylow | C19 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14563426, #100×Dic19, #14563430, … |
| maximal normal subgroup of | #14563426, #100×Dic19, #14563430, … |
| maximal quotient of | M16×C19⋊C8, #14561916, #14561922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 500);