Finite Group Databasebeta

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C₂⁴×C₃³×C₁₉ #72187162

order	8208
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4075868160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃³

Aliases

C₂⁴×C₃³×C₁₉

Subgroups

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

3752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8208 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃³×C₄×C₁₉, C₂⁵×C₃³×C₁₉, C₂⁴×C₃²×C₉×C₁₉, …
maximal normal subgroup of	C₂³×C₃³×C₄×C₁₉, C₂⁵×C₃³×C₁₉, C₂⁴×C₃²×C₉×C₁₉, …
maximal quotient of	C₂³×C₃³×C₄×C₁₉, C₂⁵×C₃³×C₁₉, C₂⁴×C₃²×C₉×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.