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C₂₇×C₃₈₃ #23780301

order	10341
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₉×C₁₉₁ (order 6876) · Inn(G) = C₁ · Out(G) = C₂²×C₉×C₁₉₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₃₄₁
abelian	C₂₇×C₃₈₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃×C₃₈₃
socle, prime radical	C₃×C₃₈₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10341 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₃₄₁, C₂×D₁₀₃₄₁
maximal subgroup of	C₈₁×C₃₈₃, C₃×C₂₇×C₃₈₃, C₂₇⋊C₃×C₃₈₃, …
maximal normal subgroup of	C₈₁×C₃₈₃, C₃×C₂₇×C₃₈₃, C₂₇⋊C₃×C₃₈₃, …
maximal quotient of	C₈₁×C₃₈₃, C₃×C₂₇×C₃₈₃, C₂×C₂₇×C₃₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10341, 1);