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C₂²×C₄×C₅×C₇₉ #72185478

order	6320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 59904
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₅×C₇₉
multiplicative	(ℤ/10461)ˣ, (ℤ/13948)ˣ, (ℤ/20922)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₅×C₇₉
socle, prime radical	C₂³×C₅×C₇₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₅×C₈×C₇₉, C₂×C₄²×C₅×C₇₉, C₂³×C₄×C₅×C₇₉, …
maximal normal subgroup of	C₂²×C₅×C₈×C₇₉, C₂×C₄²×C₅×C₇₉, C₂³×C₄×C₅×C₇₉, …
maximal quotient of	C₂²×C₅×C₈×C₇₉, C₂×C₄²×C₅×C₇₉, C₂³×C₄×C₅×C₇₉, …
automorphism group of	C₃×C₁₁×C₃₁₇
outer automorphism group of	C₃×C₁₁×C₃₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.