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C4⋊Q8×ΓL(1,𝔽16) #14322313

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

Aliases

direct productC4⋊Q8×ΓL(1,𝔽16)

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C4
HallC3×C5 ⋊ C4×C4⋊Q8
SylowC5 ⋊ Dic3×C4⋊Q8
SylowC3 ⋊ AGL(1,𝔽5)×C4⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊Q8C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4⋊Q8ΓL(1,𝔽16)
hypocenterC3×C5C4×C4⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊Q8

1176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 48011);