Finite Group Databasebeta

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C₇×C₈×C₁₉₁ #72189249

order	10696
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃×C₅×C₁₉ (order 4560) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃×C₅×C₁₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₆₉₆
abelian	C₇×C₈×C₁₉₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₁₉₁
socle, prime radical	C₂×C₇×C₁₉₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10696 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₆₉₆, D₂₁₃₉₂
maximal subgroup of	C₇×C₁₆×C₁₉₁, C₂×C₇×C₈×C₁₉₁, C₃×C₇×C₈×C₁₉₁, …
maximal normal subgroup of	C₇×C₁₆×C₁₉₁, C₂×C₇×C₈×C₁₉₁, C₃×C₇×C₈×C₁₉₁, …
maximal quotient of	C₇×C₁₆×C₁₉₁, C₂×C₇×C₈×C₁₉₁, C₃×C₇×C₈×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.