Finite Group Databasebeta

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C2×C4×#6763 #14319386

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#6763

Splittings

FittingC23×C3×C4×C5 ⋊ C4
HallC3×C5 ⋊ C2×C4×C22⋊C4
SylowC5 ⋊ C2×C4×#217
SylowC3 ⋊ C2×C4×C22⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC22×C4C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
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×C4×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

2720 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, 45084);