Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D499 |
| Fitting | C22×C4×C499 ⋊ C2 |
| derived, Sylow | C499 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D499 |
| commutator, hypocenter | C499 | C23×C4 |
| Frattini | C2 | C23×D499 |
| Fitting | C22×C4×C499 | C2 |
| socle | C23×C499 | C22 |
| prime radical | C23×D499 | C2 |
| cosocle | C2×C499 | C24 |
| LCS | G ▷ C499 | |
| UCS | C1 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
4016 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×D499, #44542945, C4×(C2×D499)⋊C4, … |
| maximal normal subgroup of | #95×D499, #44542945, C4×(C2×D499)⋊C4, … |
| maximal quotient of | C2×C42×D499, C22×C4×Dic499, C2×C22⋊C4×D499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 180);