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C3×D5×H(3,𝔽4) #14495249

order1920
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C26×C42

Aliases

direct productC3×D5×H(3,𝔽4)

Splittings

FittingC3×C5×H(3,𝔽4) ⋊ C2
HallC3×C5 ⋊ C2×H(3,𝔽4)
SylowC5 ⋊ C2×C3×H(3,𝔽4)

Subgroups

subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×H(3,𝔽4)C2
socleC22×C3×C5C25
hypercenterC3×H(3,𝔽4)D5
hypocenterC5C2×C3×H(3,𝔽4)
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×H(3,𝔽4)

2816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 220947);