C₂×C₅×C₉×C₁₃×C₂₃ #41002074

order	26910
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₆₉₁₀
abelian	C₂×C₅×C₉×C₁₃×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₁₃×C₂₃
socle, prime radical	C₂×C₃×C₅×C₁₃×C₂₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 26910

A minimal faithful permutation representation — 1 generator on 52 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)

Conjugacy classes & character table

26910 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₄₅₅, C₂×D₁₃₄₅₅
maximal subgroup of	Dic₁₃₄₅₅, C₂×D₁₃₄₅₅
maximal normal subgroup of	Dic₁₃₄₅₅, C₂×D₁₃₄₅₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 1);

C2×C5×C9×C13×C23 #41002074