Finite Group DatabasebetaFinite Group Databasebeta| order | 16528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C1033 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16861757 |
| commutator, hypocenter | C1033 | C2×C8 |
| Frattini | C2 | C2×#16861757 |
| Fitting | C4×C1033 | C4 |
| socle | C2×C1033 | C2×C4 |
| prime radical | C2×D1033 | C4 |
| cosocle | Dic1033 | C22 |
| LCS | G ▷ C1033 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8264 |
Polycyclic presentation:
2^4,1033|a^2=c,c^2=d,e^a=e^678,e^b=e^1032,e^c=e^10321048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16861757, #45683184, #45683192, … |
| maximal normal subgroup of | C8×#16861757, #45683184, #45683192, … |
| maximal quotient of | C4×#22551923, #45683187, #45683197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16528, 48);