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C₂²×C₃²×C₇×C₃₁ #21462964

order	7812
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 51840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₇×C₃₁
multiplicative	(ℤ/9121)ˣ, (ℤ/11727)ˣ, (ℤ/18242)ˣ, (ℤ/23454)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7812 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₇×C₃₁, C₂³×C₃²×C₇×C₃₁, C₂²×C₃×C₇×C₉×C₃₁, …
maximal normal subgroup of	C₂×C₃²×C₄×C₇×C₃₁, C₂³×C₃²×C₇×C₃₁, C₂²×C₃×C₇×C₉×C₃₁, …
maximal quotient of	C₂×C₃²×C₄×C₇×C₃₁, C₂³×C₃²×C₇×C₃₁, C₂²×C₃×C₇×C₉×C₃₁, …
automorphism group of	C₇×C₁₃₀₃
outer automorphism group of	C₇×C₁₃₀₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7812, 113);