C₂²×C₅×C₁₇×C₄₁ #28358278

order	13940
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₁₇×C₄₁
multiplicative	(ℤ/20913)ˣ, (ℤ/27884)ˣ, (ℤ/41826)ˣ

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 13940

A minimal faithful permutation representation — 2 generators on 67 points:

(1,2)(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);(3,4)

Conjugacy classes & character table

13940 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅×C₁₇×C₄₁, C₂³×C₅×C₁₇×C₄₁
maximal normal subgroup of	C₂×C₄×C₅×C₁₇×C₄₁, C₂³×C₅×C₁₇×C₄₁
maximal quotient of	C₂×C₄×C₅×C₁₇×C₄₁, C₂³×C₅×C₁₇×C₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13940, 13);

C22×C5×C17×C41 #28358278