Finite Group DatabasebetaFinite Group Databasebeta| order | 16096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C503 ⋊ C2 |
| Sylow | C503 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D503 |
| commutator, socle, cosocle | C22×C503 | C23 |
| Fitting | C2×Q8×C503 | C2 |
| prime radical | C2×D2012 | C2 |
| hypercenter | C2×Q8 | D503 |
| hypocenter | C503 | #124 |
| LCS | G ▷ C22×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8048 |
Polycyclic presentation:
2^5,503|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^502,f^b=f^502,f^c=f^5022524 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44566077, #44566454, #44566456, … |
| maximal normal subgroup of | #44566077, #44566454, #44566456, … |
| maximal quotient of | #44566146, #44566171, #44566182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16096, 135);