D₃×C₁₁×C₁₉ #11929422

order	1254
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₁×C₁₉
unambiguous semidirect product	C₃⋊(C₂×C₁₁×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₁×C₁₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 627

A minimal faithful permutation representation — 2 generators on 33 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);(2,3)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1254, 8);