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C3×D5×#453 #14424955

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC3×D5×#453

Splittings

FittingC3×C5×#453 ⋊ C2
HallC3×C5 ⋊ C2×#453
SylowC5 ⋊ C2×C3×#453

Subgroups

subgroupG/H
centerC2×C3D5×#120
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#453C2
socleC2×C3×C5C2×#120
hypercenterC3×#453D5
hypocenterC5C2×C3×#453
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#453

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#453, D3×D5×#453, ΓL(1,𝔽16)×#453, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×#453, D3×D5×#453, ΓL(1,𝔽16)×#453

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 150653);