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C₂×C₇×C₈×C₅₃ #72185145

order	5936
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4992
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₇×C₈×C₅₃
multiplicative	(ℤ/8907)ˣ, (ℤ/11876)ˣ, (ℤ/17814)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₇×C₅₃
socle, prime radical	C₂²×C₇×C₅₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5936 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇×C₁₆×C₅₃, C₄×C₇×C₈×C₅₃, C₂²×C₇×C₈×C₅₃, …
maximal normal subgroup of	C₂×C₇×C₁₆×C₅₃, C₄×C₇×C₈×C₅₃, C₂²×C₇×C₈×C₅₃, …
maximal quotient of	C₂×C₇×C₁₆×C₅₃, C₄×C₇×C₈×C₅₃, C₂²×C₇×C₈×C₅₃, …
automorphism group of	C₃×C₂₉₆₉
outer automorphism group of	C₃×C₂₉₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.