Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D19 |
| Fitting | C19×C32 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D19 |
| commutator, hypocenter | C19 | C2×C32 |
| Frattini | C16 | C2×D19 |
| Fitting | C19×C32 | C2 |
| socle | C2×C19 | C2×C16 |
| prime radical | C2×D19 | C16 |
| cosocle | C16×C19 | C22 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×C64, #14561845, C2×C32×D19, … |
| maximal normal subgroup of | D19×C64, #14561845, C2×C32×D19, … |
| maximal quotient of | C32×Dic19, (C2×D19)⋊C32, Dic19⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 380);