C₅×C₉×C₁₇×C₄₁ #44535850

order	31365
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₃₆₅
abelian	C₅×C₉×C₁₇×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₁₇×C₄₁
socle, prime radical	C₃×C₅×C₁₇×C₄₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 31365

A minimal faithful permutation representation — 1 generator on 72 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)

Conjugacy classes & character table

31365 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₃₁₃₆₅
Fitting subgroup of	D₃₁₃₆₅
maximal subgroup of	D₃₁₃₆₅
maximal normal subgroup of	D₃₁₃₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31365, 1);

C5×C9×C17×C41 #44535850