C₂×C₃×C₅×C₁₃×C₈₃ #44569150

order	32370
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₃₇₀
abelian	C₂×C₃×C₅×C₁₃×C₈₃
multiplicative	(ℤ/32371)ˣ, (ℤ/64742)ˣ

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 106
transitive degree	μ_t(G) = 32370

A minimal faithful permutation representation — 1 generator on 106 points:

(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106)

Conjugacy classes & character table

32370 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₆₁₈₅, C₂×D₁₆₁₈₅
socle of	Dic₁₆₁₈₅, C₂×D₁₆₁₈₅
maximal subgroup of	Dic₁₆₁₈₅, C₂×D₁₆₁₈₅
maximal normal subgroup of	Dic₁₆₁₈₅, C₂×D₁₆₁₈₅
automorphism group of	C₃₂₃₇₁
outer automorphism group of	C₃₂₃₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32370, 1);

C2×C3×C5×C13×C83 #44569150