Finite Group Databasebeta

← Prev (#72188603) Next (#72188605) →

C₈×C₁₇×C₇₃ #72188604

order	9928
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₈×C₉×C₁₆ (order 4608) · Inn(G) = C₁ · Out(G) = C₂²×C₈×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₉₂₈
abelian	C₈×C₁₇×C₇₃
multiplicative	(ℤ/9929)ˣ, (ℤ/19858)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₇×C₇₃
socle, prime radical	C₂×C₁₇×C₇₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9928 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₉₂₈, D₁₉₈₅₆
maximal subgroup of	C₁₆×C₁₇×C₇₃, C₂×C₈×C₁₇×C₇₃, C₃×C₈×C₁₇×C₇₃, …
maximal normal subgroup of	C₁₆×C₁₇×C₇₃, C₂×C₈×C₁₇×C₇₃, C₃×C₈×C₁₇×C₇₃, …
maximal quotient of	C₁₆×C₁₇×C₇₃, C₂×C₈×C₁₇×C₇₃, C₃×C₈×C₁₇×C₇₃
automorphism group of	C₉₉₂₉
outer automorphism group of	C₉₉₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.