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C₇×C₈×C₁₇₃ #72188394

order	9688
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₄₃ (order 4128) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₄₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₆₈₈
abelian	C₇×C₈×C₁₇₃
multiplicative	(ℤ/9689)ˣ, (ℤ/19378)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₁₇₃
socle, prime radical	C₂×C₇×C₁₇₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9688 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₆₈₈, D₁₉₃₇₆
maximal subgroup of	C₇×C₁₆×C₁₇₃, C₂×C₇×C₈×C₁₇₃, C₃×C₇×C₈×C₁₇₃, …
maximal normal subgroup of	C₇×C₁₆×C₁₇₃, C₂×C₇×C₈×C₁₇₃, C₃×C₇×C₈×C₁₇₃, …
maximal quotient of	C₇×C₁₆×C₁₇₃, C₂×C₇×C₈×C₁₇₃, C₃×C₇×C₈×C₁₇₃
automorphism group of	C₉₆₈₉
outer automorphism group of	C₉₆₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.