Finite Group Databasebeta

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C₂³×C₁₉×C₈₉ #72191775

order	13528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 266112
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₁₉×C₈₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₁₉×C₈₉, C₂⁴×C₁₉×C₈₉
maximal normal subgroup of	C₂²×C₄×C₁₉×C₈₉, C₂⁴×C₁₉×C₈₉
maximal quotient of	C₂²×C₄×C₁₉×C₈₉, C₂⁴×C₁₉×C₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.