Finite Group Databasebeta

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C3×AGL(1,𝔽5)×#131 #14411459

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×AGL(1,𝔽5)×#131

Splittings

FittingC3×C5×#131 ⋊ C4
HallC3×C5 ⋊ C4×#131
SylowC5 ⋊ C3×C4×#131

Subgroups

subgroupG/H
centerC3×C8C22×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C42
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC3×C5×#131C4
socleC2×C3×C5C22×C42
prime radicalC3×D5×#41C22
cosocleC4×D5C24×C3
hypercenterC3×#131AGL(1,𝔽5)
hypocenterC5C3×C4×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C3×#131

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137157);