C₉×C₄₉ #89200

order	441
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₇ (order 252) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₄₁
abelian	C₉×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₃×C₇	C₃×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

9 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 441

A minimal faithful permutation representation — 1 generator on 58 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)

Conjugacy classes & character table

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

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(441, 2);

center of	C₉×D₁₇×C₄₉, C₉×D₁₉×C₄₉, C₉×D₂₃×C₄₉, …
derived subgroup of	D₄₄₁, Dic₄₄₁, D₉×D₄₉, …
Frattini subgroup of	C₂×D₉₂₆₁
Fitting subgroup of	D₉×C₄₉, C₉×D₄₉, D₄₄₁, …
maximal subgroup of	D₉×C₄₉, C₉×D₄₉, D₄₄₁, …
maximal normal subgroup of	D₉×C₄₉, C₉×D₄₉, D₄₄₁, …
maximal quotient of	C₂×C₉×C₄₉, C₂₇×C₄₉, C₃×C₉×C₄₉, …

C9×C49 #89200