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D5×#5172 #14423481

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

Aliases

direct productD5×#5172

Splittings

FittingC2×C3×C5×SD16 ⋊ C22
HallC3×C5 ⋊ C2×#449
SylowC5 ⋊ C2×#5172
SylowC3 ⋊ D5×#449

Subgroups

subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
hypercenterC2×SD16D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

1624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 149179);