Finite Group Databasebeta

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D3×D5⋊#99 #14411911

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×D5⋊#99
unambiguous semidirect productD5⋊(D3×#99)
unambiguous semidirect product(D3×D5)⋊#99

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C22×#99
SylowC5 ⋊ C2×D3×#99
SylowC3 ⋊ C2×D5⋊#99

Subgroups

subgroupG/H
centerC2C2×D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×D3×D4×D5C2
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C22×#99
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

2224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#10604461, D3×AGL(1,𝔽5)×#99, D3×#10605017
maximal normal subgroup ofD3×#10604461, D3×AGL(1,𝔽5)×#99, D3×#10605017

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137609);