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C₂×D₃×C₈×AGL(1,𝔽₅) #14411182

order	1920
isoclinism	isoclinic class of D₃×AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂×D₃×C₈×AGL(1,𝔽₅)

Splittings

Fitting	C₂×C₃×C₅×C₈ ⋊ C₂×C₄
derived, Hall	C₃×C₅ ⋊ C₂²×C₄×C₈
Sylow	C₅ ⋊ C₂×C₄×D₃×C₈
Sylow	C₃ ⋊ C₂²×C₈×AGL(1,𝔽₅)

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₂²×C₄×C₈
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₃×C₄×D₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈

1520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 240

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₅)×#97, D₃×AGL(1,𝔽₅)×#106, C₂×D₃×D₈×AGL(1,𝔽₅)
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×#97, D₃×AGL(1,𝔽₅)×#106, C₂×D₃×D₈×AGL(1,𝔽₅)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136880);