Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×C19⋊C8 |
| Sylow | C19 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14562432, SD16×C19⋊C8, #14562439, … |
| maximal normal subgroup of | #14562432, SD16×C19⋊C8, #14562439, … |
| maximal quotient of | C4⋊C4×C19⋊C8, #14564194, #14564354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 675);