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C₅×D₃×D₇×C₂₉ #27131776

order	12180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₃×D₇×C₂₉
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₅×C₂₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₅×C₂₉)
unambiguous semidirect product	D₂₁⋊(C₂×C₅×C₂₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₂₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2175 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₇×D₉×C₂₉, C₅×D₃×C₂₉×AGL(1,𝔽₇), C₃×C₅×D₃×D₇×C₂₉, …
maximal normal subgroup of	C₅×D₃×C₂₉×AGL(1,𝔽₇), C₃×C₅×D₃×D₇×C₂₉
maximal quotient of	C₅×D₇×D₉×C₂₉, C₃×C₅×D₃×D₇×C₂₉, C₅×D₃×C₂₉×D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 111);