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C₂²×C₃×C₄²×C₁₉ #72183295

order	3648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5308416
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₃×C₄²×C₁₉
multiplicative	(ℤ/9160)ˣ, (ℤ/10992)ˣ, (ℤ/13740)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₃×C₁₉
socle, prime radical	C₂⁴×C₃×C₁₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

996 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄×C₈×C₁₉, C₂×C₃×C₄³×C₁₉, C₂³×C₃×C₄²×C₁₉, …
maximal normal subgroup of	C₂²×C₃×C₄×C₈×C₁₉, C₂×C₃×C₄³×C₁₉, C₂³×C₃×C₄²×C₁₉, …
maximal quotient of	C₂²×C₃×C₄×C₈×C₁₉, C₂×C₃×C₄³×C₁₉, C₂³×C₃×C₄²×C₁₉, …
automorphism group of	C₅×C₈×C₂₂₉, C₃×C₁₆×C₂₂₉
outer automorphism group of	C₅×C₈×C₂₂₉, C₃×C₁₆×C₂₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.