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C₃×C₄²×C₇×C₃₁ #72189071

order	10416
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 34560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₇×C₃₁
multiplicative	(ℤ/10817)ˣ, (ℤ/21634)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃×C₇×C₃₁
socle, prime radical	C₂²×C₃×C₇×C₃₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10416 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₇×C₈×C₃₁, C₂×C₃×C₄²×C₇×C₃₁, C₄²×C₇×C₉×C₃₁, …
maximal normal subgroup of	C₃×C₄×C₇×C₈×C₃₁, C₂×C₃×C₄²×C₇×C₃₁, C₄²×C₇×C₉×C₃₁, …
maximal quotient of	C₃×C₄×C₇×C₈×C₃₁, C₂×C₃×C₄²×C₇×C₃₁, C₄²×C₇×C₉×C₃₁, …
automorphism group of	C₂₉×C₃₇₃
outer automorphism group of	C₂₉×C₃₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.