D₃×C₁₃×C₃₁ #14559016

order	2418
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₃×C₃₁
unambiguous semidirect product	C₃⋊(C₂×C₁₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₁₃×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₃×C₃₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1209

A minimal faithful permutation representation — 2 generators on 47 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);(2,3)

1209 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2418, 9);