Finite Group Databasebeta

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C₇×C₈×C₁₃×C₁₉ #72192072

order	13832
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₄×C₉ (order 5184) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₄×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₈₃₂
abelian	C₇×C₈×C₁₃×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₁₃×C₁₉
socle, prime radical	C₂×C₇×C₁₃×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13832 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₈₃₂, D₂₇₆₆₄
Fitting subgroup of	D₁₃₈₃₂, Dic₆₉₁₆
maximal subgroup of	C₇×C₁₃×C₁₆×C₁₉, C₂×C₇×C₈×C₁₃×C₁₉, D₁₃₈₃₂, …
maximal normal subgroup of	C₇×C₁₃×C₁₆×C₁₉, C₂×C₇×C₈×C₁₃×C₁₉, D₁₃₈₃₂, …
maximal quotient of	C₇×C₁₃×C₁₆×C₁₉, C₂×C₇×C₈×C₁₃×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.