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C₃×D₅×D₇×C₂₉ #27131768

order	12180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₅×D₇×C₂₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₅×D₇
commutator, hypocenter	C₅×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃×C₂₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×C₂₉×D₇⋊C₉, C₉×D₅×D₇×C₂₉, C₃×D₅×C₂₉×AGL(1,𝔽₇), …
maximal normal subgroup of	D₅×C₂₉×D₇⋊C₉, C₉×D₅×D₇×C₂₉, C₃×D₅×C₂₉×AGL(1,𝔽₇), …
maximal quotient of	C₉×D₅×D₇×C₂₉, C₃²×D₅×D₇×C₂₉, C₃×D₇×C₂₉×D₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 103);