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C₇×C₁₉×ΓL(1,𝔽₁₆) #22547714

order	7980
isoclinism	isoclinic class of ΓL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×ΓL(1,𝔽₁₆)
unambiguous semidirect product	C₃⋊(C₇×C₁₉×AGL(1,𝔽₅))

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₉	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₄×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₄
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₁₉×C₉⋊AGL(1,𝔽₅), C₇×C₁₉⋊C₃×ΓL(1,𝔽₁₆), C₁₉×ΓL(1,𝔽₈)×ΓL(1,𝔽₁₆), …
maximal normal subgroup of	C₇×C₁₉⋊C₃×ΓL(1,𝔽₁₆), C₁₉×ΓL(1,𝔽₈)×ΓL(1,𝔽₁₆), ΓL(1,𝔽₁₆)×#87704, …
maximal quotient of	C₇×C₁₉×C₉⋊AGL(1,𝔽₅), C₃×C₇×C₁₉×ΓL(1,𝔽₁₆), C₇×C₁₉×C₃⋊ΓL(1,𝔽₁₆)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 139);