Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×D19 |
| Fitting | C2×Q16×C19 ⋊ C2 |
| Sylow | C19 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#358, #14565353, D19×#362, … |
| maximal normal subgroup of | D19×#358, #14565353, D19×#362, … |
| maximal quotient of | C2×#103×D19, C2×#107×D19, C4×Q16×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1324);