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C₂²×C₄²×C₈×C₁₉ #72188447

order	9728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 43486543872
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

C₂²×C₄²×C₈×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂⁵×C₁₉
socle, prime radical	C₂⁵×C₁₉	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

13188 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄²×C₁₆×C₁₉, C₂²×C₄×C₈²×C₁₉, C₂×C₄³×C₈×C₁₉, …
maximal normal subgroup of	C₂²×C₄²×C₁₆×C₁₉, C₂²×C₄×C₈²×C₁₉, C₂×C₄³×C₈×C₁₉, …
maximal quotient of	C₂²×C₄²×C₁₆×C₁₉, C₂²×C₄×C₈²×C₁₉, C₂×C₄³×C₈×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.