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C4×AGL(1,𝔽5)×#67 #14319607

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×AGL(1,𝔽5)×#67

Splittings

FittingC22×C3×C4×C5 ⋊ C2×C4
HallC3×C5 ⋊ C42×D4
SylowC5 ⋊ C42×#67
SylowC3 ⋊ C4×D4×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C42×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

1848 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, 45305);