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C₂⁴×C₃×C₄²×C₁₉ #72192740

order	14592
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4566087106560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂⁴×C₃×C₄²×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁶×C₃×C₁₉
socle, prime radical	C₂⁶×C₃×C₁₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

48060 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₄×C₈×C₁₉, C₂³×C₃×C₄³×C₁₉, C₂⁵×C₃×C₄²×C₁₉
maximal normal subgroup of	C₂⁴×C₃×C₄×C₈×C₁₉, C₂³×C₃×C₄³×C₁₉, C₂⁵×C₃×C₄²×C₁₉
maximal quotient of	C₂⁴×C₃×C₄×C₈×C₁₉, C₂³×C₃×C₄³×C₁₉, C₂⁵×C₃×C₄²×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.