Finite Group Databasebeta

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C₂×C₄²×C₁₉×C₂₃ #72192175

order	13984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 608256
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄²×C₁₉×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₁₉×C₂₃
socle, prime radical	C₂³×C₁₉×C₂₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 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	C₂×C₄×C₈×C₁₉×C₂₃, C₄³×C₁₉×C₂₃, C₂²×C₄²×C₁₉×C₂₃
maximal normal subgroup of	C₂×C₄×C₈×C₁₉×C₂₃, C₄³×C₁₉×C₂₃, C₂²×C₄²×C₁₉×C₂₃
maximal quotient of	C₂×C₄×C₈×C₁₉×C₂₃, C₄³×C₁₉×C₂₃, C₂²×C₄²×C₁₉×C₂₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.