Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D499 |
| Fitting | C2×D4×C499 ⋊ C2 |
| Sylow | C499 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D499 |
| commutator, cosocle | C2×C499 | C24 |
| Frattini | C2 | C23×D499 |
| Fitting | C2×D4×C499 | C2 |
| socle | C22×C499 | C23 |
| hypercenter | C2×D4 | D499 |
| hypocenter | C499 | C22×D4 |
| LCS | G ▷ C2×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3992 |
2510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D499, #100×D499, #102×D499, … |
| maximal normal subgroup of | #99×D499, #100×D499, #102×D499, … |
| maximal quotient of | C2×C22⋊C4×D499, C2×C4⋊C4×D499, C4×D4×D499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 182);