C₃×C₄×C₅×C₁₇×C₃₁ #44539244

order	31620
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₆₂₀
abelian	C₃×C₄×C₅×C₁₇×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₅×C₁₇×C₃₁
socle, prime radical	C₂×C₃×C₅×C₁₇×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 31620

A minimal faithful permutation representation — 1 generator on 60 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)

Conjugacy classes & character table

31620 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₈₁₀, D₃₁₆₂₀
maximal subgroup of	Dic₁₅₈₁₀, D₃₁₆₂₀
maximal normal subgroup of	Dic₁₅₈₁₀, D₃₁₆₂₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 1);

C3×C4×C5×C17×C31 #44539244