Finite Group Databasebeta

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C3×#10600897 #14301568

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

Aliases

direct productC3×#10600897

Splittings

FittingC2×C3×C5×#101 ⋊ C2
HallC3×C5 ⋊ #1888
SylowC5 ⋊ C3×#1888

Subgroups

subgroupG/H
centerC22×C3#4028
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#101C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#101D5
hypocenterC5C3×#1888
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#101

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27266);