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D5×(C2×D3)⋊C16 #14312804

order1920
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productD5×(C2×D3)⋊C16

Splittings

FittingC2×C3×C5×C16 ⋊ C22
HallC3×C5 ⋊ C2×C22⋊C16
SylowC5 ⋊ C2×(C2×D3)⋊C16
SylowC3 ⋊ D5×C22⋊C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C2×D3×D5
commutatorC2×C3×C5C22×C16
FittingC2×C3×C5×C16C22
socleC22×C3×C5C22×C8
prime radicalC22×D3×D5C8
cosocleC2×C3×C5×C8C23
hypercenterC2×C16D3×D5
hypocenterC3×C5C2×C22⋊C16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C2×C16

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38502);