Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×D4×C499 ⋊ C2 |
| Sylow | C499 ⋊ #127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D499 |
| commutator, socle, cosocle | C22×C499 | C23 |
| Fitting | C2×D4×C499 | C2 |
| hypercenter | C2×D4 | D499 |
| hypocenter | C499 | #127 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^4982504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44542890, #44543264, #44543266, … |
| maximal normal subgroup of | #44542890, #44543264, #44543266, … |
| maximal quotient of | #44542967, #44542998, #44542999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 142);