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C₈×C₁₁×C₈₉ #72186759

order	7832
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₅×C₈×C₁₁ (order 3520) · Inn(G) = C₁ · Out(G) = C₂³×C₅×C₈×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₈₃₂
abelian	C₈×C₁₁×C₈₉
multiplicative	(ℤ/7921)ˣ, (ℤ/15842)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₁×C₈₉
socle, prime radical	C₂×C₁₁×C₈₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7832 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₇₈₃₂, D₁₅₆₆₄
maximal subgroup of	C₁₁×C₁₆×C₈₉, C₂×C₈×C₁₁×C₈₉, C₃×C₈×C₁₁×C₈₉, …
maximal normal subgroup of	C₁₁×C₁₆×C₈₉, C₂×C₈×C₁₁×C₈₉, C₃×C₈×C₁₁×C₈₉, …
maximal quotient of	C₁₁×C₁₆×C₈₉, C₂×C₈×C₁₁×C₈₉, C₃×C₈×C₁₁×C₈₉
automorphism group of	C₇₉₂₁
outer automorphism group of	C₇₉₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.