Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D124 |
| Fitting | C4×Q8×C31 ⋊ C2 |
| Sylow | C31 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C4×Q8×C31 | C2 |
| prime radical | C2×D124 | C22 |
| hypercenter | C4×Q8 | D31 |
| hypocenter | C31 | D4×Q8 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16844812, #16844816, #16844874, … |
| maximal normal subgroup of | #16844812, #16844816, #16844874, … |
| maximal quotient of | Q8×(C2×D31)⋊C4, C4⋊C4×D124, Q8×C4⋊Dic31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1216);