Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×(C22⋊D19)⋊C4 |
| Fitting | C2×C22⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14561950, #14561954, #14561970, … |
| maximal normal subgroup of | #14561950, #14561954, #14561970, … |
| maximal quotient of | C2×#11926391, C2×C22⋊C4×Dic19, C2×#11926395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1007);