Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic983 |
| unambiguous semidirect product | C983⋊C42 |
| derived, Sylow | C983 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D983 |
| commutator, hypocenter | C983 | C42 |
| Frattini | C22 | C2×D983 |
| Fitting | C2×C4×C983 | C2 |
| socle, prime radical, cosocle | C22×C983 | C22 |
| LCS | G ▷ C983 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15728 |
3944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic983, #44537873, #44537889, … |
| maximal normal subgroup of | C8×Dic983, #44537873, #44537889, … |
| maximal quotient of | C983⋊#95, C8×Dic983, C4×C983⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 16);