C₁₉×C₅₃ #11758829

order	1007
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₉×C₁₃ (order 936) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₉×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₀₇
abelian	C₁₉×C₅₃

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) = 72
transitive degree	μ_t(G) = 1007

A minimal faithful permutation representation — 1 generator on 72 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)

Conjugacy classes & character table

1007 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1007, 1);

center of	D₇×C₁₉×C₅₃, D₉×C₁₉×C₅₃, C₃⋊D₃×C₁₉×C₅₃, …
derived subgroup of	D₁₀₀₇, Dic₁₀₀₇, C₁₉⋊#6157, …
Fitting subgroup of	D₁₉×C₅₃, C₁₉×D₅₃, D₁₀₀₇, …
socle of	D₁₉×C₅₃, C₁₉×D₅₃, D₁₀₀₇, …
maximal subgroup of	D₁₉×C₅₃, C₁₉×D₅₃, D₁₀₀₇, …
maximal normal subgroup of	D₁₉×C₅₃, C₁₉×D₅₃, D₁₀₀₇, …
maximal quotient of	C₂×C₁₉×C₅₃, C₃×C₁₉×C₅₃, C₁₃×C₁₉×C₅₃, …

C19×C53 #11758829