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D3×#66266 #14479113

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#66266

Splittings

FittingC3×C5×#41 ⋊ C2×C4
HallC3×C5 ⋊ C2×#520
SylowC5 ⋊ D3×#520
SylowC3 ⋊ C2×#66266

Subgroups

subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FittingC3×C5×#41C2×C4
prime radicalD3×D5×#41C2
cosocleC2×C3×D5C25
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ #41

3280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), D3×#10604863, D3×#10604003, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), D3×#10604863, D3×#10604003
maximal quotient of#72260203, #72260225

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204811);