Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10597361 |
| Fitting | C2×SD16×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10597361, #14572457, #14572471, … |
| maximal normal subgroup of | C4×#10597361, #14572457, #14572471, … |
| maximal quotient of | C2×#11926551, C2×#11926542, C2×#11926583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1340);