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C₂³×C₃×C₈×C₅₃ #72188796

order	10176
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4472832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₃×C₈×C₅₃
multiplicative	(ℤ/23968)ˣ, (ℤ/30816)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₃×C₅₃
socle, prime radical	C₂⁴×C₃×C₅₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10176 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₁₆×C₅₃, C₂²×C₃×C₄×C₈×C₅₃, C₂⁴×C₃×C₈×C₅₃, …
maximal normal subgroup of	C₂³×C₃×C₁₆×C₅₃, C₂²×C₃×C₄×C₈×C₅₃, C₂⁴×C₃×C₈×C₅₃, …
maximal quotient of	C₂³×C₃×C₁₆×C₅₃, C₂²×C₃×C₄×C₈×C₅₃, C₂⁴×C₃×C₈×C₅₃, …
automorphism group of	C₇×C₃₂×C₁₀₇, C₉×C₃₂×C₁₀₇
outer automorphism group of	C₇×C₃₂×C₁₀₇, C₉×C₃₂×C₁₀₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.