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C₃×C₄²×C₁₂₇ #72185269

order	6096
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 24192
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₁₂₇
multiplicative	(ℤ/6617)ˣ, (ℤ/13234)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃×C₁₂₇
socle, prime radical	C₂²×C₃×C₁₂₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₈×C₁₂₇, C₂×C₃×C₄²×C₁₂₇, C₄²×C₉×C₁₂₇, …
maximal normal subgroup of	C₃×C₄×C₈×C₁₂₇, C₂×C₃×C₄²×C₁₂₇, C₄²×C₉×C₁₂₇, …
maximal quotient of	C₃×C₄×C₈×C₁₂₇, C₂×C₃×C₄²×C₁₂₇, C₄²×C₉×C₁₂₇, …
automorphism group of	C₁₃×C₅₀₉
outer automorphism group of	C₁₃×C₅₀₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.