Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#11758451 |
| Fitting | C2×C42×C31 ⋊ C2 |
| Sylow | C31 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D31 |
| commutator, cosocle | C22×C31 | C24 |
| Frattini | C22 | C23×D31 |
| Fitting | C2×C42×C31 | C2 |
| socle | C23×C31 | C23 |
| hypercenter | C2×C42 | D31 |
| hypocenter | C31 | C2×#127 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#14520792, #16844378, #16844380, … |
| maximal normal subgroup of | C2×#14520792, #16844378, #16844380, … |
| maximal quotient of | C2×#14520919, C2×#14520951, C4×#11758451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1089);