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C₂²×C₅×C₁₉×ΓL(1,𝔽₈) #22547747

order	7980
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₅×C₁₉×ΓL(1,𝔽₈)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₅×C₁₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂²×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₇×C₁₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂²×C₅×C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×A₄×C₁₉×ΓL(1,𝔽₈), C₅×ΓL(1,𝔽₈)×C₂²⋊(C₁₉⋊C₃), C₂²×C₅×ΓL(1,𝔽₈)×C₁₉⋊C₃, …
maximal normal subgroup of	C₅×A₄×C₁₉×ΓL(1,𝔽₈), C₅×ΓL(1,𝔽₈)×C₂²⋊(C₁₉⋊C₃), C₂²×C₅×ΓL(1,𝔽₈)×C₁₉⋊C₃, …
maximal quotient of	C₂²×C₅×C₁₉×C₇⋊C₉, C₂×C₅×D₃×C₁₉×ΓL(1,𝔽₈), C₂²×C₃×C₅×C₁₉×ΓL(1,𝔽₈)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 172);