C₃×C₈×C₈₁ #14515698

order	1944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

abelian

C₃×C₈×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₂₇	C₂×C₃²
socle, prime radical	C₂×C₃²	C₄×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 92
transitive degree	μ_t(G) = 1944

A minimal faithful permutation representation — 2 generators on 92 points:

(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(90,91,92)

Conjugacy classes & character table

1944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₆×C₈₁, C₂×C₃×C₈×C₈₁, C₃×C₈×C₂₄₃, …
maximal normal subgroup of	C₃×C₁₆×C₈₁, C₂×C₃×C₈×C₈₁, C₃×C₈×C₂₄₃, …
maximal quotient of	C₃×C₁₆×C₈₁, C₂×C₃×C₈×C₈₁, C₃×C₈×C₂₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 92);

C3×C8×C81 #14515698