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C2×C3×#65534 #14425078

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×#65534

Splittings

FittingC2×C3×C5×2−1+4 ⋊ C2
HallC3×C5 ⋊ C2×#454
SylowC5 ⋊ C2×C3×#454

Subgroups

subgroupG/H
centerC22×C3#4099
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×2−1+4C2
socleC22×C3×C5#120
hypercenterC2×C3×2−1+4D5
hypocenterC5C2×C3×#454
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×2−1+4

1456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 150776);