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C22⋊C8×ΓL(1,𝔽16) #14295011

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C8×ΓL(1,𝔽16)

Splittings

FittingC3×C5×C22⋊C8 ⋊ C4
HallC3×C5 ⋊ C4×C22⋊C8
SylowC5 ⋊ Dic3×C22⋊C8
SylowC3 ⋊ AGL(1,𝔽5)×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×C4×D5C23
hypercenterC22⋊C8ΓL(1,𝔽16)
hypocenterC3×C5C4×C22⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22⋊C8

872 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, 20709);