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C₂×C₅×C₈×C₁₉₁ #72193289

order	15280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 12160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₅×C₈×C₁₉₁
multiplicative	(ℤ/15703)ˣ, (ℤ/31406)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₅×C₁₉₁
socle, prime radical	C₂²×C₅×C₁₉₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₁₆×C₁₉₁, C₄×C₅×C₈×C₁₉₁, C₂²×C₅×C₈×C₁₉₁
maximal normal subgroup of	C₂×C₅×C₁₆×C₁₉₁, C₄×C₅×C₈×C₁₉₁, C₂²×C₅×C₈×C₁₉₁
maximal quotient of	C₂×C₅×C₁₆×C₁₉₁, C₄×C₅×C₈×C₁₉₁, C₂²×C₅×C₈×C₁₉₁
automorphism group of	C₄₁×C₃₈₃
outer automorphism group of	C₄₁×C₃₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.