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C₂⁴×C₃×C₁₁×C₁₉ #72188703

order	10032
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7257600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂⁴×C₃×C₁₁×C₁₉
multiplicative	(ℤ/23464)ˣ, (ℤ/30168)ˣ, (ℤ/35196)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10032 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁵×C₃×C₁₁×C₁₉, C₂³×C₃×C₄×C₁₁×C₁₉, C₂⁴×C₉×C₁₁×C₁₉, …
maximal normal subgroup of	C₂⁵×C₃×C₁₁×C₁₉, C₂³×C₃×C₄×C₁₁×C₁₉, C₂⁴×C₉×C₁₁×C₁₉, …
maximal quotient of	C₂⁵×C₃×C₁₁×C₁₉, C₂³×C₃×C₄×C₁₁×C₁₉, C₂⁴×C₉×C₁₁×C₁₉, …
automorphism group of	C₇×C₈×C₄₁₉, C₈×C₉×C₄₁₉
outer automorphism group of	C₇×C₈×C₄₁₉, C₈×C₉×C₄₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.