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C₂×C₃×C₈×AGL(1,𝔽₅) #11752249

order	960
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₃×C₈×AGL(1,𝔽₅)

Splittings

Fitting	C₂×C₃×C₅×C₈ ⋊ C₄
derived, Sylow	C₅ ⋊ C₂×C₃×C₄×C₈
Hall	C₃×C₅ ⋊ C₂×C₄×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₂×C₃×C₄×C₈
Frattini	C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₄²
prime radical	C₂²×C₃×D₅	C₂×C₄
cosocle	C₄×D₅	C₂³×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈

324 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	C₃×(C₂×AGL(1,𝔽₅))⋊C₁₆, (C₂×AGL(1,𝔽₅))⋊(C₃⋊C₁₆), C₃×#10598670, …
maximal normal subgroup of	C₃×(C₂×AGL(1,𝔽₅))⋊C₁₆, (C₂×AGL(1,𝔽₅))⋊(C₃⋊C₁₆), C₃×#10598670, …
maximal quotient of	C₂×C₃×C₈×#170, C₃×C₈×D₅⋊C₈, C₂×C₃×#170⋊C₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 6444);