Finite Group Databasebeta

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#137×ΓL(1,𝔽16) #14416845

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#137×ΓL(1,𝔽16)

Splittings

FittingC3×C5×#137 ⋊ C4
HallC3×C5 ⋊ C4×#137
SylowC5 ⋊ Dic3×#137
SylowC3 ⋊ AGL(1,𝔽5)×#137

Subgroups

subgroupG/H
centerC2C2×D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC3×C5×#137C4
socleC2×C3×C5C2×C4×D4
prime radicalC3×D5×#41C22
cosocleC3×C4×D5C24
hypercenter#137ΓL(1,𝔽16)
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142543);