Finite Group Databasebeta

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C3×#10598593 #14277100

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

Aliases

direct productC3×#10598593

Splittings

HallC3×C5 ⋊ #1292
SylowC5 ⋊ C3×#1292

Subgroups

subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C3×C42
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C8C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C4⋊C4
cosocleC42×D5C22×C3
hypercenterC3×C4⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1292
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4⋊C8

304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2798);