Finite Group Databasebeta

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C5×AGL(1,𝔽5)×#104 #72275718

order3200
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×AGL(1,𝔽5)×#104

Splittings

FittingC52×#104 ⋊ C4
SylowC52 ⋊ C4×#104

Subgroups

subgroupG/H
centerC4×C5D4×AGL(1,𝔽5)
commutatorC4×C5C2×C42×C5
FrattiniC2×C4C22×C5×AGL(1,𝔽5)
FittingC52×#104C4
socleC2×C52C4×C22⋊C4
prime radicalC5×D5×#41C22
cosocleC2×C4×D5C23×C5
hypercenterC5×#104AGL(1,𝔽5)
hypocenterC5C4×C5×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C5×#104

742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×#453, #104×AGL(1,ℤ/25)
maximal normal subgroup ofC5×AGL(1,𝔽5)×#453
maximal quotient of#104×AGL(1,ℤ/25)

GAP

Past the SmallGroups library coverage — no SmallGroups id.