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D₃×C₂₉×D₃₅ #27131804

order	12180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₂₉×D₃₅
unambiguous semidirect product	(C₅×D₃)⋊(D₇×C₂₉)
unambiguous semidirect product	(D₃×C₇)⋊(D₅×C₂₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₃×D₃₅
commutator, hypocenter	C₃×C₅×C₇	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₂₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₂₉×D₃₅, D₃×C₂₉×C₅⋊AGL(1,𝔽₇), C₃×D₃×C₂₉×D₃₅, …
maximal normal subgroup of	D₃×C₂₉×C₅⋊AGL(1,𝔽₇), C₃×D₃×C₂₉×D₃₅
maximal quotient of	D₉×C₂₉×D₃₅, C₃×D₃×C₂₉×D₃₅, D₃×C₂₉×D₁₀₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 139);