Finite Group Databasebeta

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C22×Q8×ΓL(1,𝔽16) #14478850

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×ΓL(1,𝔽16)
unambiguous semidirect productD5⋊(C2×Q8×Dic3)

Splittings

FittingC22×C3×C5×Q8 ⋊ C4
HallC3×C5 ⋊ C22×C4×Q8
SylowC5 ⋊ C22×Q8×Dic3
SylowC3 ⋊ C22×Q8×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C24×C4
FrattiniC2C24×ΓL(1,𝔽16)
FittingC22×C3×C5×Q8C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC2×C3×D5C25
hypercenterC22×Q8ΓL(1,𝔽16)
hypocenterC3×C5C22×C4×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

3328 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, 204548);