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C₂²×C₉×C₁₃×C₂₃ #24924477

order	10764
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9504
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₉×C₁₃×C₂₃
multiplicative	(ℤ/11381)ˣ, (ℤ/16173)ˣ, (ℤ/22762)ˣ, (ℤ/32346)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₁₃×C₂₃
socle, prime radical	C₂²×C₃×C₁₃×C₂₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10764 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₉×C₁₃×C₂₃, C₂³×C₉×C₁₃×C₂₃, C₂²×C₁₃×C₂₃×C₂₇, …
maximal normal subgroup of	C₂×C₄×C₉×C₁₃×C₂₃, C₂³×C₉×C₁₃×C₂₃, C₂²×C₁₃×C₂₃×C₂₇, …
maximal quotient of	C₂×C₄×C₉×C₁₃×C₂₃, C₂³×C₉×C₁₃×C₂₃, C₂²×C₁₃×C₂₃×C₂₇, …
automorphism group of	C₁₉×C₅₉₉, C₂×C₂₇×C₅₉₉
outer automorphism group of	C₁₉×C₅₉₉, C₂×C₂₇×C₅₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 13);