C₃³×C₉×C₆₁ #28415015

order	14823
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁶

Aliases

abelian

C₃³×C₉×C₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃⁴×C₆₁
socle, prime radical	C₃⁴×C₆₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 14823

A minimal faithful permutation representation — 4 generators on 79 points:

(1,2,3,4,5,6,7,8,9)(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);(10,11,12);(13,14,15);(16,17,18)

Conjugacy classes & character table

14823 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃³×C₉×C₆₁
maximal normal subgroup of	C₂×C₃³×C₉×C₆₁
maximal quotient of	C₂×C₃³×C₉×C₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14823, 61);

C33×C9×C61 #28415015