C₂²×C₅×C₉×C₇₃ #27190179

order	13140
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₉×C₇₃
multiplicative	(ℤ/19713)ˣ, (ℤ/26284)ˣ, (ℤ/39426)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₅×C₇₃
socle, prime radical	C₂²×C₃×C₅×C₇₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 13140

A minimal faithful permutation representation — 2 generators on 91 points:

(1,2)(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);(3,4)

Conjugacy classes & character table

13140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅×C₉×C₇₃, C₂³×C₅×C₉×C₇₃
maximal normal subgroup of	C₂×C₄×C₅×C₉×C₇₃, C₂³×C₅×C₉×C₇₃
maximal quotient of	C₂×C₄×C₅×C₉×C₇₃, C₂³×C₅×C₉×C₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13140, 13);

C22×C5×C9×C73 #27190179