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C₂×D₅×C₁₉×ΓL(1,𝔽₈) #22547689

order	7980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₅×C₁₉×ΓL(1,𝔽₈)
unambiguous semidirect product	C₅⋊(C₂²×C₁₉×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₁₉×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₇×D₅)⋊(C₃×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₅×ΓL(1,𝔽₈)
commutator, hypocenter	C₅×C₇	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₅×ΓL(1,𝔽₈)×C₁₉⋊C₃, D₃×D₅×C₁₉×ΓL(1,𝔽₈), C₂×C₃×D₅×C₁₉×ΓL(1,𝔽₈), …
maximal normal subgroup of	C₂×D₅×ΓL(1,𝔽₈)×C₁₉⋊C₃, C₂×C₃×D₅×C₁₉×ΓL(1,𝔽₈)
maximal quotient of	C₂×D₅×C₁₉×C₇⋊C₉, D₃×D₅×C₁₉×ΓL(1,𝔽₈), C₂×C₃×D₅×C₁₉×ΓL(1,𝔽₈), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 114);