Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D4×C19⋊C8 |
| Sylow | C19 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14562427, D8×C19⋊C8, SD16×C19⋊C8, … |
| maximal normal subgroup of | #14562427, D8×C19⋊C8, SD16×C19⋊C8, … |
| maximal quotient of | D8×C19⋊C8, SD16×C19⋊C8, Q16×C19⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 615);