Finite Group Databasebeta

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C4×#91221 #14294212

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C42

Aliases

direct productC4×#91221

Splittings

FittingC3×C4×C5×C8 ⋊ C4
HallC3×C5 ⋊ C4×#97
SylowC5 ⋊ C4×#815
SylowC3 ⋊ C4×#3992

Subgroups

subgroupG/H
centerC42C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C43
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×D5C23
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5C4×#97
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C42 ◁ C4×C8

720 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, 19910);