Finite Group Databasebeta

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C4×#91931 #14411279

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#91931

Splittings

HallC3×C5 ⋊ C2×C4×M16
SylowC5 ⋊ C4×D3×M16
SylowC3 ⋊ C4×D5⋊M16

Subgroups

subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC23×D15C2×C4
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136977);