Finite Group Databasebeta

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C4×D32×AGL(1,𝔽5) #72230264

order2880
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D32×AGL(1,𝔽5)

Splittings

FittingC32×C4×C5 ⋊ C22×C4
derived, HallC32×C5 ⋊ C22×C42
SylowC32 ⋊ C22×C4×AGL(1,𝔽5)
SylowC5 ⋊ C42×D32

Subgroups

subgroupG/H
center, hypercenterC4D32×AGL(1,𝔽5)
commutator, hypocenterC32×C5C22×C42
FrattiniC2C2×D32×AGL(1,𝔽5)
FittingC32×C4×C5C22×C4
socleC2×C32×C5C23×C4
prime radicalC2×D32×D5C22
cosocleC2×C32×D5C24
LCSG ▷ C32×C5
UCSC1 ◁ C4

2100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×D4×AGL(1,𝔽5), AGL(1,𝔽5)×#64306, D32×AGL(1,𝔽5)2, …
maximal normal subgroup ofD32×D4×AGL(1,𝔽5), AGL(1,𝔽5)×#64306, AGL(1,𝔽5)×#64312
maximal quotient ofD32×AGL(1,𝔽5)2, D3×AGL(1,𝔽5)×#624

GAP

Past the SmallGroups library coverage — no SmallGroups id.