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C₉×C₁₃×C₆₄ #72186449

order	7488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄×C₁₆ (order 2304) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₄₈₈
abelian	C₉×C₁₃×C₆₄
multiplicative	(ℤ/7489)ˣ, (ℤ/14978)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₃₂	C₂×C₃×C₁₃
socle, prime radical	C₂×C₃×C₁₃	C₃×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

42 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7488 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₄₉₇₆, Dic₇₄₈₈
maximal subgroup of	C₉×C₁₃×C₁₂₈, C₂×C₉×C₁₃×C₆₄, C₁₃×C₂₇×C₆₄, …
maximal normal subgroup of	C₉×C₁₃×C₁₂₈, C₂×C₉×C₁₃×C₆₄, C₁₃×C₂₇×C₆₄, …
maximal quotient of	C₉×C₁₃×C₁₂₈, C₂×C₉×C₁₃×C₆₄, C₁₃×C₂₇×C₆₄, …
automorphism group of	C₇₄₈₉
outer automorphism group of	C₇₄₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.