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C₂³×C₄×C₇×C₄₇ #72189136

order	10528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5935104
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₄×C₇×C₄₇
multiplicative	(ℤ/26360)ˣ, (ℤ/31632)ˣ, (ℤ/39540)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₇×C₄₇
socle, prime radical	C₂⁴×C₇×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₇×C₈×C₄₇, C₂²×C₄²×C₇×C₄₇, C₂⁴×C₄×C₇×C₄₇, …
maximal normal subgroup of	C₂³×C₇×C₈×C₄₇, C₂²×C₄²×C₇×C₄₇, C₂⁴×C₄×C₇×C₄₇, …
maximal quotient of	C₂³×C₇×C₈×C₄₇, C₂²×C₄²×C₇×C₄₇, C₂⁴×C₄×C₇×C₄₇, …
automorphism group of	C₅×C₈×C₆₅₉, C₃×C₁₆×C₆₅₉
outer automorphism group of	C₅×C₈×C₆₅₉, C₃×C₁₆×C₆₅₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.