Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C499 ⋊ C2 |
| Sylow | C499 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D499 |
| commutator, socle | C2×C499 | C22×C4 |
| Fitting | M16×C499 | C2 |
| prime radical | #22547811 | C2 |
| cosocle | C4×C499 | C23 |
| hypercenter | M16 | D499 |
| hypocenter | C499 | #131 |
| LCS | G ▷ C2×C499 ▷ C499 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|a^2=d,d^2=e,f^a=f^498,c^b=ce,f^c=f^4982510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44543212, #44543214, #44543217, … |
| maximal normal subgroup of | #44543212, #44543214, #44543217, … |
| maximal quotient of | #44543055, #44543056, #44543063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 154);