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C₂²×C₃×C₄×C₅³ #72185203

order	6000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 571392000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅³

Aliases

abelian	C₂²×C₃×C₄×C₅³
multiplicative	(ℤ/8525)ˣ, (ℤ/17050)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃×C₅³
socle, prime radical	C₂³×C₃×C₅³	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

3456 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₅³×C₈, C₂×C₃×C₄²×C₅³, C₂³×C₃×C₄×C₅³, …
maximal normal subgroup of	C₂²×C₃×C₅³×C₈, C₂×C₃×C₄²×C₅³, C₂³×C₃×C₄×C₅³, …
maximal quotient of	C₂²×C₃×C₅³×C₈, C₂×C₃×C₄²×C₅³, C₂³×C₃×C₄×C₅³, …
automorphism group of	C₁₁×C₂₅×C₃₁
outer automorphism group of	C₁₁×C₂₅×C₃₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.