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C2×C4⋊C4×ΓL(1,𝔽16) #14319443

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×ΓL(1,𝔽16)

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C4
HallC3×C5 ⋊ C2×C4×C4⋊C4
SylowC5 ⋊ C2×Dic3×C4⋊C4
SylowC3 ⋊ C2×C4⋊C4×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5C2×C4×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 45141);