Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D983 |
| unambiguous semidirect product | C23⋊D983 |
| Fitting | C23×C983 ⋊ C2 |
| Sylow | C983 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D983 |
| commutator, cosocle | C2×C983 | C23 |
| Frattini | C2 | C22×D983 |
| Fitting | C23×C983 | C2 |
| socle | C22×C983 | C22 |
| hypercenter | C23 | D983 |
| hypocenter | C983 | C2×D4 |
| LCS | G ▷ C2×C983 ▷ C983 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
3938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44537877, (C22⋊D983)⋊C4, C4×C22⋊D983, … |
| maximal normal subgroup of | #44537877, (C22⋊D983)⋊C4, C4×C22⋊D983, … |
| maximal quotient of | C2×(C2×D983)⋊C4, C2×C22⋊Dic983, C2×Dic983⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 35);