Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#10597336 |
| Sylow | C19 ⋊ C2×#125 |
226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14564589, #14564591, #14564598, … |
| maximal normal subgroup of | #14564589, #14564591, #14564598, … |
| maximal quotient of | C2×#11926409, C2×#11926427, C2×#11926431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1070);