Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D31 |
| unambiguous semidirect product | C31⋊C26 |
| unambiguous semidirect product | (C2×C31)⋊C25 |
| Fitting, socle | C25×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D31 |
| commutator, cosocle, hypocenter | C31 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×#379, C2×#14520904, #16853987, … |
| maximal normal subgroup of | D31×#379, C2×#14520904, #16853987, … |
| maximal quotient of | C24×C4×D31, C25×Dic31, C23×D4×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1387);