Finite Group Databasebeta

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C2×AGL(1,𝔽5)×#235 #14478946

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,𝔽5)×#235
unambiguous semidirect productD5⋊(C4×#235)

Splittings

FittingC22×C3×C4×C5 ⋊ C2×C4
HallC3×C5 ⋊ C2×C4×#41
SylowC5 ⋊ C2×C4×#235
SylowC3 ⋊ C2×#41×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#235C2
cosocleC2×C3×D5C25
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

3456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204644);