Finite Group Databasebeta

← Prev (#23778305) Next (#23778307) →

C₄×C₁₇×C₁₄₉ #23778306

order	10132
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₁₆×C₃₇ (order 4736) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₁₆×C₃₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₁₃₂
abelian	C₄×C₁₇×C₁₄₉
multiplicative	(ℤ/10133)ˣ, (ℤ/20266)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₇×C₁₄₉
socle, prime radical	C₂×C₁₇×C₁₄₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10132 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₁₃₂, D₂₀₂₆₄
maximal subgroup of	C₃×C₄×C₁₇×C₁₄₉, Dic₃×C₁₇×C₁₄₉, C₈×C₁₇×C₁₄₉, …
maximal normal subgroup of	C₃×C₄×C₁₇×C₁₄₉, C₈×C₁₇×C₁₄₉, C₂×C₄×C₁₇×C₁₄₉, …
maximal quotient of	C₃×C₄×C₁₇×C₁₄₉, Dic₃×C₁₇×C₁₄₉, C₈×C₁₇×C₁₄₉, …
automorphism group of	C₁₀₁₃₃
outer automorphism group of	C₁₀₁₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10132, 1);