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C₂²×C₃²×C₄²×C₁₉ #72189496

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 127401984
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₃×C₄

Aliases

abelian	C₂²×C₃²×C₄²×C₁₉
multiplicative	(ℤ/23816)ˣ, (ℤ/24045)ˣ, (ℤ/25648)ˣ, (ℤ/32060)ˣ, (ℤ/32976)ˣ, (ℤ/35724)ˣ, (ℤ/41220)ˣ, (ℤ/48090)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₃²×C₁₉
socle, prime radical	C₂⁴×C₃²×C₁₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

2988 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	C₂²×C₃²×C₄×C₈×C₁₉, C₂×C₃²×C₄³×C₁₉, C₂³×C₃²×C₄²×C₁₉
maximal normal subgroup of	C₂²×C₃²×C₄×C₈×C₁₉, C₂×C₃²×C₄³×C₁₉, C₂³×C₃²×C₄²×C₁₉
maximal quotient of	C₂²×C₃²×C₄×C₈×C₁₉, C₂×C₃²×C₄³×C₁₉, C₂³×C₃²×C₄²×C₁₉
automorphism group of	C₈×C₁₃×C₂₂₉, C₇×C₁₆×C₂₂₉
outer automorphism group of	C₈×C₁₃×C₂₂₉, C₇×C₁₆×C₂₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.