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D3×D5×C4⋊C8 #14412976

order1920
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD3×D5×C4⋊C8

Splittings

FittingC3×C5×C4⋊C8 ⋊ C22
HallC3×C5 ⋊ C22×C4⋊C8
SylowC5 ⋊ C2×D3×C4⋊C8
SylowC3 ⋊ C2×D5×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutatorC2×C3×C5C23×C8
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C23×C4
prime radicalC22×D3×D5C2×C4
cosocleC2×C3×C4×C5C24
hypercenterC4⋊C8D3×D5
hypocenterC3×C5C22×C4⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4⋊C8

1280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138674);