C₁₉×C₁₀₉ #14523406

order	2071
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₉×C₂₇ (order 1944) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₉×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₀₇₁
abelian	C₁₉×C₁₀₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 128
transitive degree	μ_t(G) = 2071

A minimal faithful permutation representation — 1 generator on 128 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)

Conjugacy classes & character table

2071 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2071, 1);

center of	D₅×C₁₉×C₁₀₉, A₄×C₁₉×C₁₀₉, D₇×C₁₉×C₁₀₉, …
derived subgroup of	D₂₀₇₁, #32916114, #32916115, …
Fitting subgroup of	D₁₉×C₁₀₉, C₁₉×D₁₀₉, D₂₀₇₁, …
socle of	D₁₉×C₁₀₉, C₁₉×D₁₀₉, D₂₀₇₁, …
maximal subgroup of	D₁₉×C₁₀₉, C₁₉×D₁₀₉, D₂₀₇₁, …
maximal normal subgroup of	D₁₉×C₁₀₉, C₁₉×D₁₀₉, D₂₀₇₁, …
maximal quotient of	C₂×C₁₉×C₁₀₉, C₇×C₁₉×C₁₀₉, C₁₁×C₁₉×C₁₀₉, …

C19×C109 #14523406