C₄×C₅×C₃₇×C₄₁ #44476809

order	30340
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₀₃₄₀
abelian	C₄×C₅×C₃₇×C₄₁
multiplicative	(ℤ/30341)ˣ, (ℤ/60682)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₃₇×C₄₁
socle, prime radical	C₂×C₅×C₃₇×C₄₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 30340

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

30340 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₁₇₀, D₃₀₃₄₀
maximal subgroup of	Dic₁₅₁₇₀, D₃₀₃₄₀
maximal normal subgroup of	Dic₁₅₁₇₀, D₃₀₃₄₀
automorphism group of	C₃₀₃₄₁
outer automorphism group of	C₃₀₃₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30340, 1);

C4×C5×C37×C41 #44476809