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C₂×C₃²×C₄×C₈×C₁₉ #72189490

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1769472
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

abelian	C₂×C₃²×C₄×C₈×C₁₉
multiplicative	(ℤ/15995)ˣ, (ℤ/17823)ˣ, (ℤ/20565)ˣ, (ℤ/23764)ˣ, (ℤ/31990)ˣ, (ℤ/35646)ˣ, (ℤ/41130)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₃²×C₁₉
socle, prime radical	C₂³×C₃²×C₁₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

972 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₁₆×C₁₉, C₂×C₃²×C₈²×C₁₉, C₃²×C₄²×C₈×C₁₉, …
maximal normal subgroup of	C₂×C₃²×C₄×C₁₆×C₁₉, C₂×C₃²×C₈²×C₁₉, C₃²×C₄²×C₈×C₁₉, …
maximal quotient of	C₂×C₃²×C₄×C₁₆×C₁₉, C₂×C₃²×C₈²×C₁₉, C₃²×C₄²×C₈×C₁₉, …
automorphism group of	C₅×C₇×C₄₅₇
outer automorphism group of	C₅×C₇×C₄₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.