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C₂²×C₃×C₉×C₁₀₇ #72190010

order	11556
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 68688
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃×C₉×C₁₀₇
multiplicative	(ℤ/12217)ˣ, (ℤ/17361)ˣ, (ℤ/24434)ˣ, (ℤ/34722)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃²×C₁₀₇
socle, prime radical	C₂²×C₃²×C₁₀₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11556 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₉×C₁₀₇, C₂³×C₃×C₉×C₁₀₇
maximal normal subgroup of	C₂×C₃×C₄×C₉×C₁₀₇, C₂³×C₃×C₉×C₁₀₇
maximal quotient of	C₂×C₃×C₄×C₉×C₁₀₇, C₂³×C₃×C₉×C₁₀₇
automorphism group of	C₁₉×C₆₄₃
outer automorphism group of	C₁₉×C₆₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.