Finite Group Databasebeta

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C2×#11752380 #14413302

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#11752380
unambiguous semidirect productD5⋊#5106

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C2×#427
SylowC5 ⋊ C2×#5106
SylowC3 ⋊ C2×#65721

Subgroups

subgroupG/H
centerC2×C4C4⋊ΓL(1,𝔽16)
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×D5D4
cosocleC3×C4×D5C24
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5C2×#427
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

1024 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, 139000);