Finite Group Databasebeta

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C₂²×C₄×C₁₃×C₄₇ #72188488

order	9776
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 105984
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₁₃×C₄₇
multiplicative	(ℤ/18345)ˣ, (ℤ/19568)ˣ, (ℤ/24460)ˣ, (ℤ/36690)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₁₃×C₄₇
socle, prime radical	C₂³×C₁₃×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9776 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₁₃×C₄₇, C₂×C₄²×C₁₃×C₄₇, C₂³×C₄×C₁₃×C₄₇, …
maximal normal subgroup of	C₂²×C₈×C₁₃×C₄₇, C₂×C₄²×C₁₃×C₄₇, C₂³×C₄×C₁₃×C₄₇, …
maximal quotient of	C₂²×C₈×C₁₃×C₄₇, C₂×C₄²×C₁₃×C₄₇, C₂³×C₄×C₁₃×C₄₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.