Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D983 |
| Fitting | C8×C983 ⋊ C2 |
| derived, Sylow | C983 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D983 |
| commutator, hypocenter | C983 | C2×C8 |
| Frattini | C4 | C2×D983 |
| Fitting | C8×C983 | C2 |
| socle | C2×C983 | C2×C4 |
| prime radical | C2×D983 | C4 |
| cosocle | C4×C983 | C22 |
| LCS | G ▷ C983 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
3944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D983, #44537902, C2×C8×D983, … |
| maximal normal subgroup of | C16×D983, #44537902, C2×C8×D983, … |
| maximal quotient of | C8×Dic983, (C2×D983)⋊C8, Dic983⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 21);