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C₂×C₉×C₆₅₃ #26044359

order	11754
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₇₅₄
abelian	C₂×C₉×C₆₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₆₅₃
socle, prime radical	C₂×C₃×C₆₅₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11754 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₇₅₄, D₂₃₅₀₈
Fitting subgroup of	Dic₉×C₆₅₃, C₉×Dic₆₅₃, Dic₅₈₇₇, …
maximal subgroup of	C₄×C₉×C₆₅₃, Dic₉×C₆₅₃, C₉×Dic₆₅₃, …
maximal normal subgroup of	C₄×C₉×C₆₅₃, Dic₉×C₆₅₃, C₉×Dic₆₅₃, …
maximal quotient of	C₄×C₉×C₆₅₃, C₂²×C₉×C₆₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11754, 1);