Finite Group Databasebeta

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C₈×C₁₁×C₁₅₇ #72191979

order	13816
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₅×C₁₃ (order 6240) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₅×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₈₁₆
abelian	C₈×C₁₁×C₁₅₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₁×C₁₅₇
socle, prime radical	C₂×C₁₁×C₁₅₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13816 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₈₁₆, D₂₇₆₃₂
Fitting subgroup of	D₁₃₈₁₆, Dic₆₉₀₈
maximal subgroup of	C₁₁×C₁₆×C₁₅₇, C₂×C₈×C₁₁×C₁₅₇, D₁₃₈₁₆, …
maximal normal subgroup of	C₁₁×C₁₆×C₁₅₇, C₂×C₈×C₁₁×C₁₅₇, D₁₃₈₁₆, …
maximal quotient of	C₁₁×C₁₆×C₁₅₇, C₂×C₈×C₁₁×C₁₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.