C₂×C₃×C₅×C₂₉×C₃₇ #44565708

order	32190
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₁₉₀
abelian	C₂×C₃×C₅×C₂₉×C₃₇
multiplicative	(ℤ/32191)ˣ, (ℤ/64382)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) = 76
transitive degree	μ_t(G) = 32190

A minimal faithful permutation representation — 1 generator on 76 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)

Conjugacy classes & character table

32190 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₆₀₉₅, C₂×D₁₆₀₉₅
socle of	Dic₁₆₀₉₅, C₂×D₁₆₀₉₅
maximal subgroup of	Dic₁₆₀₉₅, C₂×D₁₆₀₉₅
maximal normal subgroup of	Dic₁₆₀₉₅, C₂×D₁₆₀₉₅
automorphism group of	C₃₂₁₉₁
outer automorphism group of	C₃₂₁₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 1);

C2×C3×C5×C29×C37 #44565708