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C₅×D₃×D₂₀₃ #27131778

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

Aliases

direct product	C₅×D₃×D₂₀₃
unambiguous semidirect product	(D₃×C₇)⋊(C₅×D₂₉)
unambiguous semidirect product	(D₃×C₂₉)⋊(C₅×D₇)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₃×D₂₀₃
commutator, hypocenter	C₃×C₇×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₅

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1545 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₉×D₂₀₃, C₅×D₃×ΓL(1,𝔽₈)⋊D₂₉, C₃×C₅×D₃×D₂₀₃, …
maximal normal subgroup of	C₅×D₃×ΓL(1,𝔽₈)⋊D₂₉, C₃×C₅×D₃×D₂₀₃
maximal quotient of	C₅×D₉×D₂₀₃, C₃×C₅×D₃×D₂₀₃, C₅×D₃×D₆₀₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 113);