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C₄×C₈×C₁₃×C₂₃ #72188281

order	9568
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 33792
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₈×C₁₃×C₂₃
multiplicative	(ℤ/11965)ˣ, (ℤ/23930)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₁₃×C₂₃
socle, prime radical	C₂²×C₁₃×C₂₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9568 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₁₃×C₁₆×C₂₃, C₈²×C₁₃×C₂₃, C₂×C₄×C₈×C₁₃×C₂₃, …
maximal normal subgroup of	C₄×C₁₃×C₁₆×C₂₃, C₈²×C₁₃×C₂₃, C₂×C₄×C₈×C₁₃×C₂₃, …
maximal quotient of	C₄×C₁₃×C₁₆×C₂₃, C₈²×C₁₃×C₂₃, C₂×C₄×C₈×C₁₃×C₂₃, …
automorphism group of	C₅×C₂₃₉₃
outer automorphism group of	C₅×C₂₃₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.