Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C31⋊C8 |
| derived, Sylow | C31 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D31 |
| commutator, hypocenter | C31 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D31 |
| Fitting | C2×C42×C31 | C2 |
| socle, prime radical | C23×C31 | C2×C4 |
| cosocle | C2×C4×C31 | C23 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31⋊#1273, #16843545, #16843547, … |
| maximal normal subgroup of | C31⋊#1273, #16843545, #16843547, … |
| maximal quotient of | C2×C8×C31⋊C8, C2×#14520770, M16×C31⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 495);