Finite Group Databasebeta

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C₁₃×C₁₆×C₆₇ #72192147

order	13936
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄²×C₁₁ (order 6336) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄²×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₉₃₆
abelian	C₁₃×C₁₆×C₆₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₃×C₆₇
socle, prime radical	C₂×C₁₃×C₆₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13936 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₉₃₆, D₂₇₈₇₂
Fitting subgroup of	D₁₃₉₃₆, Dic₆₉₆₈
maximal subgroup of	C₁₃×C₃₂×C₆₇, C₂×C₁₃×C₁₆×C₆₇, D₁₃₉₃₆, …
maximal normal subgroup of	C₁₃×C₃₂×C₆₇, C₂×C₁₃×C₁₆×C₆₇, D₁₃₉₃₆, …
maximal quotient of	C₁₃×C₃₂×C₆₇, C₂×C₁₃×C₁₆×C₆₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.