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C₂²×C₃³×C₄×C₁₇ #72186368

order	7344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 34504704
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂²×C₃³×C₄×C₁₇
multiplicative	(ℤ/9373)ˣ, (ℤ/12051)ˣ, (ℤ/18746)ˣ, (ℤ/24102)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃³×C₁₇
socle, prime radical	C₂³×C₃³×C₁₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

1512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7344 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃³×C₈×C₁₇, C₂×C₃³×C₄²×C₁₇, C₂³×C₃³×C₄×C₁₇, …
maximal normal subgroup of	C₂²×C₃³×C₈×C₁₇, C₂×C₃³×C₄²×C₁₇, C₂³×C₃³×C₄×C₁₇, …
maximal quotient of	C₂²×C₃³×C₈×C₁₇, C₂×C₃³×C₄²×C₁₇, C₂³×C₃³×C₄×C₁₇, …
automorphism group of	C₇×C₁₃×C₁₀₃
outer automorphism group of	C₇×C₁₃×C₁₀₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.