Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×Dic31 |
| derived, Sylow | C31 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D31 |
| commutator, hypocenter | C31 | C4×C16 |
| Frattini | C2×C8 | C2×D31 |
| Fitting | C2×C16×C31 | C2 |
| socle, prime radical | C22×C31 | C2×C8 |
| cosocle | C2×C8×C31 | C22 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C16 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic31, #16843844, Dic31⋊C32, … |
| maximal normal subgroup of | C32×Dic31, #16843844, Dic31⋊C32, … |
| maximal quotient of | C16×C31⋊C8, #16843630, #16843788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 322);