Finite Group Databasebeta

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C2×D5⋊#812 #14478089

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

Aliases

direct productC2×D5⋊#812
unambiguous semidirect productD5⋊(C2×#812)

Splittings

HallC3×C5 ⋊ C22×M32
SylowC5 ⋊ C22×#812
SylowC3 ⋊ C2×D5⋊M32

Subgroups

subgroupG/H
centerC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C23×C8
FrattiniC4C23×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC22×C3×C5C22×C8
prime radicalC23×C3×D5C8
cosocleC3×#168C24
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5C22×M32
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C22×C8

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 203787);