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Cayley diagram

D5×SD16 #4059

order160
automorphismAut(G) = C22×D4×AGL(1,𝔽5) (order 640) · Inn(G) = D4×D5 · Out(G) = C23
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productD5×SD16

Splittings

FittingC5×SD16 ⋊ C2
SylowC5 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC2D4×D5
commutator, cosocleC4×C5C23
FrattiniC4C22×D5
FittingC5×SD16C2
socleC2×C5C2×D4
prime radicalD4×D5C2
hypercenterSD16D5
hypocenterC5C2×SD16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C4 ◁ SD16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 40

A minimal faithful permutation representation — 3 generators on 13 points:

(2,5)(3,8)(6,7)(9,10,12,13,11);(1,2,4,7)(3,5,8,6);(10,11)(12,13)

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofSD16×AGL(1,𝔽5), #65735, C2×D5×SD16, …
maximal normal subgroup ofSD16×AGL(1,𝔽5), #65735, C2×D5×SD16, …
maximal quotient of#65047, #65049, #65050, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 134);