C₂×C₁₁×C₂₃×C₅₃ #41001202

order	26818
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₆₈₁₈
abelian	C₂×C₁₁×C₂₃×C₅₃

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) = 89
transitive degree	μ_t(G) = 26818

A minimal faithful permutation representation — 1 generator on 89 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)

Conjugacy classes & character table

26818 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₄₀₉, C₂×D₁₃₄₀₉
socle of	Dic₁₃₄₀₉, C₂×D₁₃₄₀₉
maximal subgroup of	Dic₁₃₄₀₉, C₂×D₁₃₄₀₉
maximal normal subgroup of	Dic₁₃₄₀₉, C₂×D₁₃₄₀₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26818, 1);

C2×C11×C23×C53 #41001202