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C2×D5⋊#798 #14478106

order1920
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×D5⋊#798
unambiguous semidirect productD5⋊(C2×#798)

Splittings

HallC3×C5 ⋊ C22×M32
SylowC5 ⋊ C22×#798
SylowC3 ⋊ C2×D5⋊M32

Subgroups

subgroupG/H
center, hypercenterC2×C8D3×AGL(1,𝔽5)
commutatorC2×C3×C5C23×C8
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C22×C8
prime radicalC22×D3×D5C8
cosocleC3×#168C24
hypocenterC3×C5C22×M32
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 203804);