Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C499 ⋊ C2 |
| Sylow | C499 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D499 |
| commutator, socle, cosocle | C22×C499 | C23 |
| Fitting | C2×Q8×C499 | C2 |
| prime radical | C2×D1996 | C2 |
| hypercenter | C2×Q8 | D499 |
| hypocenter | C499 | #124 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^498,f^b=f^498,f^c=f^4982504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44542894, #44543271, #44543273, … |
| maximal normal subgroup of | #44542894, #44543271, #44543273, … |
| maximal quotient of | #44542963, #44542988, #44542999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 135);