Finite Group Databasebeta

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C2×#11751966 #14416401

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

Aliases

direct productC2×#11751966
unambiguous semidirect productD5⋊#4817

Splittings

FittingC2×C3×C5×Q8 ⋊ C2×C4
HallC3×C5 ⋊ C2×#440
SylowC5 ⋊ C2×#4817
SylowC3 ⋊ C2×#65735

Subgroups

subgroupG/H
centerC22#67⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×D5×D12C22
cosocleC3×C4×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#440
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

1088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142099);