Finite Group Databasebeta

← Prev (#72188493) Next (#72188495) →

C₄×C₉×C₁₆×C₁₇ #72188494

order	9792
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 24576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₉×C₁₆×C₁₇
multiplicative	(ℤ/10421)ˣ, (ℤ/10693)ˣ, (ℤ/20842)ˣ, (ℤ/21386)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₈	C₂²×C₃×C₁₇
socle, prime radical	C₂²×C₃×C₁₇	C₂×C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9792 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₁₇×C₃₂, C₈×C₉×C₁₆×C₁₇, C₂×C₄×C₉×C₁₆×C₁₇, …
maximal normal subgroup of	C₄×C₉×C₁₇×C₃₂, C₈×C₉×C₁₆×C₁₇, C₂×C₄×C₉×C₁₆×C₁₇, …
maximal quotient of	C₄×C₉×C₁₇×C₃₂, C₈×C₉×C₁₆×C₁₇, C₂×C₄×C₉×C₁₆×C₁₇, …
automorphism group of	C₁₇×C₆₁₃, C₃₇×C₂₈₉
outer automorphism group of	C₁₇×C₆₁₃, C₃₇×C₂₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.