Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D983 |
| Fitting | C2×C4×C983 ⋊ C2 |
| derived, Sylow | C983 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D983 |
| commutator, hypocenter | C983 | C22×C4 |
| Frattini | C2 | C22×D983 |
| Fitting | C2×C4×C983 | C2 |
| socle | C22×C983 | C22 |
| prime radical | C22×D983 | C2 |
| cosocle | C2×C983 | C23 |
| LCS | G ▷ C983 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
3944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D983)⋊C8, C42×D983, C22⋊C4×D983, … |
| maximal normal subgroup of | (C2×D983)⋊C8, C42×D983, C22⋊C4×D983, … |
| maximal quotient of | C42×D983, C2×C4×Dic983, C22⋊C4×D983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 32);