Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10597396 |
| Fitting | C2×#41×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×#135 |
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 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) = 608 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14563959, #14563960, #14563962, … |
| maximal normal subgroup of | #14563959, #14563960, #14563962, … |
| maximal quotient of | C2×#11926538, C2×#11926540, C2×#11926580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1329);