C₅×C₉×C₂₃×C₃₁ #44545539

order	32085
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₀₈₅
abelian	C₅×C₉×C₂₃×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₂₃×C₃₁
socle, prime radical	C₃×C₅×C₂₃×C₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 68
transitive degree	μ_t(G) = 32085

A minimal faithful permutation representation — 1 generator on 68 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)

Conjugacy classes & character table

32085 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₃₂₀₈₅
Fitting subgroup of	D₃₂₀₈₅
maximal subgroup of	D₃₂₀₈₅
maximal normal subgroup of	D₃₂₀₈₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32085, 1);

C5×C9×C23×C31 #44545539