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C₂²×C₄×C₇×C₃₁ #72183149

order	3472
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 34560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₄×C₇×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₇×C₃₁
socle, prime radical	C₂³×C₇×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₇×C₃₁, C₂²×C₇×C₈×C₃₁, C₂³×C₄×C₇×C₃₁, …
maximal normal subgroup of	C₂×C₄²×C₇×C₃₁, C₂²×C₇×C₈×C₃₁, C₂³×C₄×C₇×C₃₁, …
maximal quotient of	C₂×C₄²×C₇×C₃₁, C₂²×C₇×C₈×C₃₁, C₂³×C₄×C₇×C₃₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.