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#104×ΓL(1,𝔽16) #14295588

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#104×ΓL(1,𝔽16)

Splittings

FittingC3×C5×#104 ⋊ C4
HallC3×C5 ⋊ C4×#104
SylowC5 ⋊ Dic3×#104
SylowC3 ⋊ AGL(1,𝔽5)×#104

Subgroups

subgroupG/H
centerC4D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#104C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC3×D5×#41C22
cosocleC2×C3×C4×D5C23
hypercenter#104ΓL(1,𝔽16)
hypocenterC3×C5C4×#104
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽16)×#453, D3×AGL(1,𝔽5)×#104, #72229778, …
maximal normal subgroup ofΓL(1,𝔽16)×#453, D3×AGL(1,𝔽5)×#104, #72229778
maximal quotient of#72260193, #72260271

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21286);