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C₂×C₄×C₁₃×C₇₁ #72186392

order	7384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₁₃×C₇₁
multiplicative	(ℤ/9235)ˣ, (ℤ/18470)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₁₃×C₇₁
socle, prime radical	C₂²×C₁₃×C₇₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₁₃×C₇₁, C₄²×C₁₃×C₇₁, C₂²×C₄×C₁₃×C₇₁, …
maximal normal subgroup of	C₂×C₈×C₁₃×C₇₁, C₄²×C₁₃×C₇₁, C₂²×C₄×C₁₃×C₇₁, …
maximal quotient of	C₂×C₈×C₁₃×C₇₁, C₄²×C₁₃×C₇₁, C₂²×C₄×C₁₃×C₇₁, …
automorphism group of	C₅×C₁₈₄₇
outer automorphism group of	C₅×C₁₈₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.