Finite Group Databasebeta

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#41×D5⋊AGL(1,𝔽5) #72220988

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#41×D5⋊AGL(1,𝔽5)

Splittings

FittingC52×#41 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC4C22×D5⋊AGL(1,𝔽5)
commutator, socleC2×C52C24×C4
FrattiniC2C23×D5⋊AGL(1,𝔽5)
FittingC52×#41C2×C4
prime radicalD52×#41C2
cosocleC2×C5⋊D5C25
hypercenter#41D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ #41

3766 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×D5⋊AGL(1,𝔽5), #72223009, #72223047
maximal normal subgroup ofAGL(1,ℤ/8)×D5⋊AGL(1,𝔽5), #72223009, #72223047
maximal quotient of#121×D5⋊AGL(1,𝔽5)

GAP

Past the SmallGroups library coverage — no SmallGroups id.