Finite Group Databasebeta

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C3×#10602577 #14301487

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10602577

Splittings

HallC3×C5 ⋊ #1886
SylowC5 ⋊ C3×#1886

Subgroups

subgroupG/H
centerC22×C3#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×C4⋊Q8C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4⋊Q8D5
hypocenterC5C3×#1886
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊Q8

648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27185);