Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#10597393 |
| Fitting | C22×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14564020, #14564036, #14564038, … |
| maximal normal subgroup of | #14564020, #14564036, #14564038, … |
| maximal quotient of | C2×#11926409, C2×#11926434, C2×#11926445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1067);