Finite Group Databasebeta

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C₂×C₃×C₄×C₈×C₃₁ #72185159

order	5952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 122880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₃×C₄×C₈×C₃₁
multiplicative	(ℤ/11936)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₃×C₃₁
socle, prime radical	C₂³×C₃×C₃₁	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5952 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₁₆×C₃₁, C₂×C₃×C₈²×C₃₁, C₃×C₄²×C₈×C₃₁, …
maximal normal subgroup of	C₂×C₃×C₄×C₁₆×C₃₁, C₂×C₃×C₈²×C₃₁, C₃×C₄²×C₈×C₃₁, …
maximal quotient of	C₂×C₃×C₄×C₁₆×C₃₁, C₂×C₃×C₈²×C₃₁, C₃×C₄²×C₈×C₃₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.