Finite Group Databasebeta

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C3×#10604174 #14294874

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct productC3×#10604174

Splittings

HallC3×C5 ⋊ #1744
SylowC5 ⋊ C3×#1744

Subgroups

subgroupG/H
centerC22×C3×C4C2×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C3×#1744
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20572);