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C2×D3×#3993 #14413261

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×#3993
unambiguous semidirect productD5⋊(D3×#106)
unambiguous semidirect product(D3×D5)⋊#106

Splittings

FittingC2×C3×C5×C8 ⋊ C2×C4
HallC3×C5 ⋊ C22×#106
SylowC5 ⋊ C2×D3×#106
SylowC3 ⋊ C22×#3993

Subgroups

subgroupG/H
centerC22D3×C4⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×D3×D5D4
cosocleC3×C4×D5C24
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C22×#106
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#106
maximal normal subgroup ofD3×AGL(1,𝔽5)×#106

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138959);