Finite Group Databasebeta

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C3×#10617560 #14412917

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10617560

Splittings

FittingC3×C5×H(5,𝔽2) ⋊ C4
HallC3×C5 ⋊ #2901
SylowC5 ⋊ C3×#2901

Subgroups

subgroupG/H
centerC2×C3C22×C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC3×C5×H(5,𝔽2)C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC3×#66285C2
cosocleC4×D5C24×C3
hypercenterC3×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C3×#2901
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×#41 ◁ C3×H(5,𝔽2)

1476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138615);