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C₉×Dic₁₆₉ #20258698

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

Aliases

C₉×Dic₁₆₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₆₉
commutator, hypocenter	C₁₆₉	C₄×C₉
Frattini, socle	C₂×C₃×C₁₃	C₃×D₁₃
Fitting	C₂×C₉×C₁₆₉	C₂
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₂×C₉

27 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1548 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×Dic₁₆₉, C₉×Dic₈₄₅, C₉×#16809979
maximal normal subgroup of	C₅×C₉×Dic₁₆₉
maximal quotient of	C₅×C₉×Dic₁₆₉, C₉×Dic₈₄₅, C₉×#16809979

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 5);