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C5⋊D5×AGL(1,ℤ/16) #72253111

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5

Aliases

direct productC5⋊D5×AGL(1,ℤ/16)

Splittings

FittingC52×AGL(1,ℤ/16) ⋊ C2
SylowC52 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2C5⋊D5×#442
commutatorC52×C8C23×C4
FrattiniC2×C8C23×C5⋊D5
FittingC52×AGL(1,ℤ/16)C2
socleC2×C52C2×#442
prime radicalC5⋊D5×#509C2
cosocleC2×C52×C8C24
hypercenterAGL(1,ℤ/16)C5⋊D5
hypocenterC52C2×AGL(1,ℤ/16)
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

2840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

322 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#1043×AGL(1,ℤ/16)
maximal normal subgroup of#1043×AGL(1,ℤ/16)
maximal quotient ofC5⋊D5×#12067

GAP

Past the SmallGroups library coverage — no SmallGroups id.