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C₇×C₉×C₁₈₁ #26037547

order	11403
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₄₀₃
abelian	C₇×C₉×C₁₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₇×C₁₈₁
socle, prime radical	C₃×C₇×C₁₈₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11403 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₄₀₃
Fitting subgroup of	C₇×C₉×D₁₈₁, C₉×D₇×C₁₈₁, C₉×D₁₂₆₇, …
maximal subgroup of	C₂×C₇×C₉×C₁₈₁, C₇×C₉×D₁₈₁, C₉×D₇×C₁₈₁, …
maximal normal subgroup of	C₂×C₇×C₉×C₁₈₁, C₇×C₉×D₁₈₁, C₉×D₇×C₁₈₁, …
maximal quotient of	C₂×C₇×C₉×C₁₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11403, 1);