Finite Group Databasebeta

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C3×#10601226 #14285019

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10601226

Splittings

FittingC2×C3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ #1551
SylowC5 ⋊ C3×#1551

Subgroups

subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65811C2
cosocleC42×C5C23×C3
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C3×#1551
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 10717);