C₂×C₁₃×C₁₉×C₅₃ #39910499

order	26182
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₆₁₈₂
abelian	C₂×C₁₃×C₁₉×C₅₃
multiplicative	(ℤ/26183)ˣ, (ℤ/52366)ˣ

Subgroups

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

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 26182

A minimal faithful permutation representation — 1 generator on 87 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)

Conjugacy classes & character table

26182 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₀₉₁, C₂×D₁₃₀₉₁
socle of	Dic₁₃₀₉₁, C₂×D₁₃₀₉₁
maximal subgroup of	Dic₁₃₀₉₁, C₂×D₁₃₀₉₁
maximal normal subgroup of	Dic₁₃₀₉₁, C₂×D₁₃₀₉₁
automorphism group of	C₂₆₁₈₃
outer automorphism group of	C₂₆₁₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26182, 1);

C2×C13×C19×C53 #39910499