Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10597378 |
| Fitting | C22×D4×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
202 conjugacy classes — view the full character table.
| maximal subgroup of | #14564008, #14564014, #14564112, … |
| maximal normal subgroup of | #14564008, #14564014, #14564112, … |
| maximal quotient of | C2×#11926549, C2×#11926543, C2×#11926584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1336);