Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#64545 |
| Fitting | C4×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C4×#41 |
310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14562016, #14562021, #14562068, … |
| maximal normal subgroup of | #14562016, #14562021, #14562068, … |
| maximal quotient of | C4×#10597338, C4×#10597339, C4×Q8×Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1019);