Finite Group Databasebeta

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C₃×C₇×C₈×C₈₃ #72192152

order	13944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁵×C₃×C₄₁ (order 3936) · Inn(G) = C₁ · Out(G) = C₂⁵×C₃×C₄₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₉₄₄
abelian	C₃×C₇×C₈×C₈₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₇×C₈₃
socle, prime radical	C₂×C₃×C₇×C₈₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13944 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₉₄₄, D₂₇₈₈₈
Fitting subgroup of	D₁₃₉₄₄, Dic₆₉₇₂
maximal subgroup of	C₃×C₇×C₁₆×C₈₃, C₂×C₃×C₇×C₈×C₈₃, D₁₃₉₄₄, …
maximal normal subgroup of	C₃×C₇×C₁₆×C₈₃, C₂×C₃×C₇×C₈×C₈₃, D₁₃₉₄₄, …
maximal quotient of	C₃×C₇×C₁₆×C₈₃, C₂×C₃×C₇×C₈×C₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.