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C₄×C₁₆₉⋊C₉ #20258696

order	6084
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₁₆₉⋊C₉
unambiguous semidirect product	(C₄×C₁₆₉)⋊C₉

Splittings

derived, Sylow	C₁₆₉ ⋊ C₄×C₉
Hall	C₄×C₁₆₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	C₁₆₉⋊C₃
commutator, hypocenter	C₁₆₉	C₄×C₉
Frattini, socle	C₂×C₃×C₁₃	C₂×C₁₃⋊C₃
Fitting	C₃×C₄×C₁₆₉	C₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₃×C₄

27 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

708 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×C₁₆₉⋊C₉, C₄×C₅×C₁₆₉⋊C₉, AGL(1,𝔽₅)×C₁₆₉⋊C₉
maximal normal subgroup of	C₄×C₅×C₁₆₉⋊C₉
maximal quotient of	Dic₅×C₁₆₉⋊C₉, C₄×C₅×C₁₆₉⋊C₉, AGL(1,𝔽₅)×C₁₆₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 3);