Finite Group Databasebeta

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C3×#10598171 #14277205

order1920
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10598171

Splittings

HallC3×C5 ⋊ #1298
SylowC5 ⋊ C3×#1298

Subgroups

subgroupG/H
centerC2×C3×C4#685
commutatorC2×C4×C5C3×C42
FrattiniC23×C4C2×C3×D5
FittingC2×C3×C5×C22⋊C8C2
socleC22×C3×C5#95
prime radicalC24×C3×C5Q8
cosocleC23×C4×C5C22×C3
hypercenterC2×C3×C22⋊C8D5
hypocenterC5C3×#1298
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 2903);