Finite Group Databasebeta

← Prev (#72192172) Next (#72192174) →

C₄×C₈×C₁₉×C₂₃ #72192173

order	13984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 50688
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

C₄×C₈×C₁₉×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₁₉×C₂₃
socle, prime radical	C₂²×C₁₉×C₂₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

88 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	C₄×C₁₆×C₁₉×C₂₃, C₈²×C₁₉×C₂₃, C₂×C₄×C₈×C₁₉×C₂₃
maximal normal subgroup of	C₄×C₁₆×C₁₉×C₂₃, C₈²×C₁₉×C₂₃, C₂×C₄×C₈×C₁₉×C₂₃
maximal quotient of	C₄×C₁₆×C₁₉×C₂₃, C₈²×C₁₉×C₂₃, C₂×C₄×C₈×C₁₉×C₂₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.