Finite Group Databasebeta

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C3×#10601220 #14281919

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

Aliases

direct productC3×#10601220

Splittings

FittingC2×C3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ #1483
SylowC5 ⋊ C3×#1483

Subgroups

subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C4
cosocleC42×C5C23×C3
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C3×#1483
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7617);