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C2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽5) #72275696

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽5)

Splittings

FittingC2×C4×C52 ⋊ C42
SylowC52 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22C2×AGL(1,𝔽5)2
commutatorC2×C52C22×C42
FrattiniC2C22×AGL(1,𝔽5)2
FittingC2×C4×C52C42
socleC22×C52C2×C42
prime radicalC22×D52C23
cosocleC2×D52C24
hypercenterC2×C4AGL(1,𝔽5)2
hypocenterC52C2×C4×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4

1902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.