Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C491 ⋊ C2 |
| Sylow | C491 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D491 |
| commutator, socle, cosocle | C22×C491 | C23 |
| Fitting | C2×Q8×C491 | C2 |
| prime radical | C2×D1964 | C2 |
| hypercenter | C2×Q8 | D491 |
| hypocenter | C491 | #124 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^490,f^b=f^490,f^c=f^4902464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536521, #44536898, #44536900, … |
| maximal normal subgroup of | #44536521, #44536898, #44536900, … |
| maximal quotient of | #44536590, #44536615, #44536626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 135);