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C3×AGL(1,𝔽5)×#104 #14295587

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×AGL(1,𝔽5)×#104

Splittings

FittingC3×C5×#104 ⋊ C4
HallC3×C5 ⋊ C4×#104
SylowC5 ⋊ C3×C4×#104

Subgroups

subgroupG/H
centerC3×C4D4×AGL(1,𝔽5)
commutatorC4×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#104C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC3×D5×#41C22
cosocleC2×C4×D5C23×C3
hypercenterC3×#104AGL(1,𝔽5)
hypocenterC5C3×C4×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#104

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#453, D3×AGL(1,𝔽5)×#104, AGL(1,𝔽5)×#4822, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×#453, D3×AGL(1,𝔽5)×#104, AGL(1,𝔽5)×#4822
maximal quotient ofC3×#72213321, C3×AGL(1,𝔽5)×#805

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21285);