Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×Dic19 |
| derived, Sylow | C19 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D19 |
| commutator, hypocenter | C19 | C4×C16 |
| Frattini | C2×C8 | C2×D19 |
| Fitting | C2×C16×C19 | C2 |
| socle, prime radical | C22×C19 | C2×C8 |
| cosocle | C2×C8×C19 | C22 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C16 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic19, #14561768, Dic19⋊C32, … |
| maximal normal subgroup of | C32×Dic19, #14561768, Dic19⋊C32, … |
| maximal quotient of | C16×C19⋊C8, #14561554, #14561712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 322);