Finite Group Databasebeta

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C3×#10603908 #14295053

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10603908

Splittings

FittingC3×C5×C22⋊C8 ⋊ C4
HallC3×C5 ⋊ #1749
SylowC5 ⋊ C3×#1749

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×D5C2×C4
cosocleC2×C4×D5C23×C3
hypercenterC3×C22⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1749
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C22⋊C8

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 20751);