Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C499 ⋊ C2 |
| Sylow | C499 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D499 |
| commutator, cosocle | C4×C499 | C23 |
| Frattini | C4 | C22×D499 |
| Fitting | D8×C499 | C2 |
| socle | C2×C499 | C2×D4 |
| hypercenter | D8 | D499 |
| hypocenter | C499 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C499 ▷ C2×C499 ▷ C499 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3992 |
Polycyclic presentation:
2^5,499|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^4981754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D499, C2×#30630375, #44543894, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D499, C2×#30630375, #44543894, … |
| maximal quotient of | #44543096, #44543101, #44543139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 170);