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C₂²×C₅²×C₉×C₁₃ #26043347

order	11700
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 207360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂²×C₅²×C₉×C₁₃
multiplicative	(ℤ/12881)ˣ, (ℤ/25762)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₅²×C₁₃
socle, prime radical	C₂²×C₃×C₅²×C₁₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅²×C₉×C₁₃, C₂³×C₅²×C₉×C₁₃
maximal normal subgroup of	C₂×C₄×C₅²×C₉×C₁₃, C₂³×C₅²×C₉×C₁₃
maximal quotient of	C₂×C₄×C₅²×C₉×C₁₃, C₂³×C₅²×C₉×C₁₃
automorphism group of	C₁₁×C₁₁₇₁
outer automorphism group of	C₁₁×C₁₁₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 194);