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AGL(1,𝔽5)×#904 #14416305

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#904

Splittings

FittingC2×C3×C5×C8 ⋊ C2×C4
HallC3×C5 ⋊ C4×#135
SylowC5 ⋊ C4×#904
SylowC3 ⋊ AGL(1,𝔽5)×#135

Subgroups

subgroupG/H
centerC4AGL(1,𝔽5)×D12
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#904C2
cosocleC3×C4×D5C24
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

1000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142003);