Finite Group Databasebeta

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C₇×C₂₇×C₄₃ #72187012

order	8127
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₇×C₉ (order 4536) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₇×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₁₂₇
abelian	C₇×C₂₇×C₄₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃×C₇×C₄₃
socle, prime radical	C₃×C₇×C₄₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8127 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₁₂₇, C₂×D₈₁₂₇
maximal subgroup of	C₂×C₇×C₂₇×C₄₃, C₇×C₄₃×C₈₁, C₃×C₇×C₂₇×C₄₃, …
maximal normal subgroup of	C₂×C₇×C₂₇×C₄₃, C₇×C₄₃×C₈₁, C₃×C₇×C₂₇×C₄₃, …
maximal quotient of	C₂×C₇×C₂₇×C₄₃, C₇×C₄₃×C₈₁, C₃×C₇×C₂₇×C₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.