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C₂³×C₄×C₁₉×C₂₃ #72192176

order	13984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8515584
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₄×C₁₉×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₁₉×C₂₃
socle, prime radical	C₂⁴×C₁₉×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

472 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₈×C₁₉×C₂₃, C₂²×C₄²×C₁₉×C₂₃, C₂⁴×C₄×C₁₉×C₂₃
maximal normal subgroup of	C₂³×C₈×C₁₉×C₂₃, C₂²×C₄²×C₁₉×C₂₃, C₂⁴×C₄×C₁₉×C₂₃
maximal quotient of	C₂³×C₈×C₁₉×C₂₃, C₂²×C₄²×C₁₉×C₂₃, C₂⁴×C₄×C₁₉×C₂₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.