Finite Group Databasebeta

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C2×#11752347 #14320131

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

Aliases

direct productC2×#11752347
unambiguous semidirect productD5⋊#4935

Splittings

FittingC2×C3×C42×C5 ⋊ C4
HallC3×C5 ⋊ C2×#384
SylowC5 ⋊ C2×#4935
SylowC3 ⋊ C2×#65688

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5C2×#384
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

1776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45829);