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C₂²×C₄×C₅×C₁₇₃ #72192078

order	13840
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 132096
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₅×C₁₇₃
multiplicative	(ℤ/19085)ˣ, (ℤ/26025)ˣ, (ℤ/27688)ˣ, (ℤ/34700)ˣ, (ℤ/38170)ˣ, (ℤ/41532)ˣ, (ℤ/52050)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₅×C₁₇₃
socle, prime radical	C₂³×C₅×C₁₇₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 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	C₂×C₄²×C₅×C₁₇₃, C₂²×C₅×C₈×C₁₇₃, C₂³×C₄×C₅×C₁₇₃
maximal normal subgroup of	C₂×C₄²×C₅×C₁₇₃, C₂²×C₅×C₈×C₁₇₃, C₂³×C₄×C₅×C₁₇₃
maximal quotient of	C₂×C₄²×C₅×C₁₇₃, C₂²×C₅×C₈×C₁₇₃, C₂³×C₄×C₅×C₁₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.