Finite Group Databasebeta

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C2×#11752423 #14319880

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#11752423
unambiguous semidirect productD5⋊#5211

Splittings

FittingC23×C3×C4×C5 ⋊ C4
HallC3×C5 ⋊ C2×#381
SylowC5 ⋊ C2×#5211
SylowC3 ⋊ C2×#65764

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC23×C3×C4×C5C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC22×C3×D5C24
hypercenterC23×C4ΓL(1,𝔽16)
hypocenterC3×C5C2×#381
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

2288 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, 45578);