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C₃×C₄₉×C₇₃ #24924351

order	10731
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₇×C₈×C₉ (order 6048) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₇×C₈×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₇₃₁
abelian	C₃×C₄₉×C₇₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₃×C₇×C₇₃
socle, prime radical	C₃×C₇×C₇₃	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10731 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₇₃₁
Fitting subgroup of	C₃×C₄₉×D₇₃, C₃×C₇₃×D₄₉, C₃×D₃₅₇₇, …
maximal subgroup of	C₂×C₃×C₄₉×C₇₃, C₃×C₄₉×D₇₃, C₃×C₇₃×D₄₉, …
maximal normal subgroup of	C₂×C₃×C₄₉×C₇₃, C₃×C₄₉×D₇₃, C₃×C₇₃×D₄₉, …
maximal quotient of	C₂×C₃×C₄₉×C₇₃, C₉×C₄₉×C₇₃, C₃²×C₄₉×C₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10731, 1);