Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D31 |
| Fitting | C31×C32 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D31 |
| commutator, hypocenter | C31 | C2×C32 |
| Frattini | C16 | C2×D31 |
| Fitting | C31×C32 | C2 |
| socle | C2×C31 | C2×C16 |
| prime radical | C2×D31 | C16 |
| cosocle | C16×C31 | C22 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×C64, #16843921, C2×C32×D31, … |
| maximal normal subgroup of | D31×C64, #16843921, C2×C32×D31, … |
| maximal quotient of | C32×Dic31, (C2×D31)⋊C32, Dic31⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 380);