C₁₉×C₄₉ #11745396

order	931
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₇×C₉ (order 756) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₇×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₃₁
abelian	C₁₉×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₇×C₁₉
socle, prime radical	C₇×C₁₉	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 68
transitive degree	μ_t(G) = 931

A minimal faithful permutation representation — 1 generator on 68 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)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68)

Conjugacy classes & character table

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

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(931, 1);

center of	D₉×C₁₉×C₄₉, C₃⋊D₃×C₁₉×C₄₉, C₁₉×AGL(1,𝔽₅)×C₄₉, …
derived subgroup of	D₉₃₁, #14584107, #14584108, …
Fitting subgroup of	C₁₉×D₄₉, D₁₉×C₄₉, D₉₃₁, …
maximal subgroup of	C₁₉×D₄₉, D₁₉×C₄₉, D₉₃₁, …
maximal normal subgroup of	C₁₉×D₄₉, D₁₉×C₄₉, D₉₃₁, …
maximal quotient of	C₂×C₁₉×C₄₉, C₃×C₁₉×C₄₉, C₅×C₁₉×C₄₉, …

C19×C49 #11745396