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C₄×C₇×C₁₆×C₁₉ #72187385

order	8512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 27648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₇×C₁₆×C₁₉
multiplicative	(ℤ/10645)ˣ, (ℤ/21290)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂²×C₇×C₁₉
socle, prime radical	C₂²×C₇×C₁₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

116 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇×C₁₉×C₃₂, C₇×C₈×C₁₆×C₁₉, C₂×C₄×C₇×C₁₆×C₁₉, …
maximal normal subgroup of	C₄×C₇×C₁₉×C₃₂, C₇×C₈×C₁₆×C₁₉, C₂×C₄×C₇×C₁₆×C₁₉, …
maximal quotient of	C₄×C₇×C₁₉×C₃₂, C₇×C₈×C₁₆×C₁₉, C₂×C₄×C₇×C₁₆×C₁₉, …
automorphism group of	C₅×C₂₁₂₉
outer automorphism group of	C₅×C₂₁₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.