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C3×AGL(1,𝔽5)×#127 #14322257

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC3×AGL(1,𝔽5)×#127

Splittings

FittingC3×C5×#127 ⋊ C4
HallC3×C5 ⋊ C4×#127
SylowC5 ⋊ C3×C4×#127

Subgroups

subgroupG/H
centerC22×C3C23×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC3×C5×#127C4
socleC22×C3×C5C23×C4
prime radicalC3×D5×#127C2
cosocleC22×D5C24×C3
hypercenterC3×#127AGL(1,𝔽5)
hypocenterC5C3×C4×#127
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#127

1848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#127, C3×AGL(1,𝔽5)×#453, AGL(1,𝔽5)×#5077, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×#127, C3×AGL(1,𝔽5)×#453, AGL(1,𝔽5)×#5077, …
maximal quotient ofC3×#127×#1043, C32×AGL(1,𝔽5)×#127

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47955);