Finite Group Databasebeta

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#117×ΓL(1,𝔽16) #14319501

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×ΓL(1,𝔽16)

Splittings

FittingC3×C5×#117 ⋊ C4
HallC3×C5 ⋊ C4×#117
SylowC5 ⋊ Dic3×#117
SylowC3 ⋊ AGL(1,𝔽5)×#117

Subgroups

subgroupG/H
centerC2×C4C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC3×C5×#117C4
socleC22×C3×C5C23×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenter#117ΓL(1,𝔽16)
hypocenterC3×C5C4×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #117

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45199);