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C₂₇×C₃₈₉ #24901873

order	10503
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₉×C₉₇ (order 6984) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₉×C₉₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₀₃
abelian	C₂₇×C₃₈₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃×C₃₈₉
socle, prime radical	C₃×C₃₈₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10503 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₀₃, C₂×D₁₀₅₀₃
maximal subgroup of	C₈₁×C₃₈₉, C₃×C₂₇×C₃₈₉, C₂₇⋊C₃×C₃₈₉, …
maximal normal subgroup of	C₈₁×C₃₈₉, C₃×C₂₇×C₃₈₉, C₂₇⋊C₃×C₃₈₉, …
maximal quotient of	C₈₁×C₃₈₉, C₃×C₂₇×C₃₈₉, C₂×C₂₇×C₃₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10503, 1);