Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#10597394 |
| Sylow | C19 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14563437, #14563438, #14563473, … |
| maximal normal subgroup of | #14563437, #14563438, #14563473, … |
| maximal quotient of | C2×#11926500, C4×#10597394, C2×#11926511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1312);