Finite Group DatabasebetaFinite Group Databasebeta| order | 16528 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1033 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22551925 |
| commutator, hypocenter | C1033 | C16 |
| Fitting, socle, prime radical | C2×C1033 | C8 |
| cosocle | #22551923 | C2 |
| LCS | G ▷ C1033 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16528 |
Polycyclic presentation:
2^4,1033|a^2=b,b^2=c,c^2=d,e^a=e^802,e^b=e^678,e^c=e^1032274 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30658337, #45683225, #45683226, … |
| maximal normal subgroup of | C2×#30658337, #45683225, #45683226, … |
| maximal quotient of | #45683220, C2×#30658337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16528, 52);