Finite Group Databasebeta

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C4×C4⋊(C3⋊#170) #14296101

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊(C3⋊#170)

Splittings

HallC3×C5 ⋊ C4×C4⋊C8
SylowC5 ⋊ C4×C4⋊(C3⋊C8)
SylowC3 ⋊ C4×C4⋊#170

Subgroups

subgroupG/H
centerC22×C4C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×Dic5C23
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5C4×C4⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21799);