Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D31 |
| Fitting | C22×C8×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D31 |
| commutator, hypocenter | C31 | C23×C8 |
| Frattini | C4 | C23×D31 |
| Fitting | C22×C8×C31 | C2 |
| socle | C23×C31 | C2×C4 |
| prime radical | C23×D31 | C4 |
| cosocle | C4×C31 | C24 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×#336, #16845406, D31×#340, … |
| maximal normal subgroup of | D31×#336, #16845406, D31×#340, … |
| maximal quotient of | C2×C4×C8×D31, C22×C8×Dic31, C2×C22⋊C8×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1305);