Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of #64525 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#64527 |
| Fitting | C22×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14563966, #14563972, #14563988, … |
| maximal normal subgroup of | #14563966, #14563972, #14563988, … |
| maximal quotient of | C22×#10597266, C22×#10597292, C22×#10597265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1321);