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C₄²×C₅×C₁₇₃ #72192077

order	13840
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 66048
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₅×C₁₇₃
multiplicative	(ℤ/17305)ˣ, (ℤ/34610)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₅×C₁₇₃
socle, prime radical	C₂²×C₅×C₁₇₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₈×C₁₇₃, C₂×C₄²×C₅×C₁₇₃
maximal normal subgroup of	C₄×C₅×C₈×C₁₇₃, C₂×C₄²×C₅×C₁₇₃
maximal quotient of	C₄×C₅×C₈×C₁₇₃, C₂×C₄²×C₅×C₁₇₃
automorphism group of	C₅×C₃₄₆₁
outer automorphism group of	C₅×C₃₄₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.