Finite Group Databasebeta

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C3×#10604726 #14295514

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#10604726

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ #1757
SylowC5 ⋊ C3×#1757

Subgroups

subgroupG/H
centerC3×C8C22⋊AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×C3×#709C22
cosocleC2×C4×D5C23×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1757
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×C8 ◁ C22×C3×C8

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21212);