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C3×D5⋊(D4⋊C8) #14281484

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24

Aliases

direct productC3×D5⋊(D4⋊C8)
unambiguous semidirect productD5⋊(C3×D4⋊C8)

Splittings

HallC3×C5 ⋊ C2×D4⋊C8
SylowC5 ⋊ C2×C3×D4⋊C8

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C3×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4×D4AGL(1,𝔽5)
hypocenterC5C2×C3×D4⋊C8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×D4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 7182);