Finite Group Databasebeta

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C2×C3×D5×#100 #14412039

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D5×#100

Splittings

FittingC2×C3×C5×#100 ⋊ C2
HallC3×C5 ⋊ C22×#100
SylowC5 ⋊ C22×C3×#100

Subgroups

subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#100C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#100D5
hypocenterC5C22×C3×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 137737);