Finite Group Databasebeta

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C4×#91160 #14296646

order1920
isoclinismisoclinic class of #91159
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#91160

Splittings

HallC3×C5 ⋊ C4×#107
SylowC5 ⋊ C4×#807
SylowC3 ⋊ C4×#3994

Subgroups

subgroupG/H
centerC2×C4Dic3⋊AGL(1,𝔽5)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#107
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22344);