D₃×C₁₉² #14524218

order	2166
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉² · Schur multiplier (H₂) = C₁₉

Aliases

direct product	D₃×C₁₉²
unambiguous semidirect product	C₃⋊(C₂×C₁₉²)

Fitting, socle, Hall	C₃×C₁₉² ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉²

	subgroup	G/H
center, hypercenter	C₁₉²	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₉²
Frattini	C₁	G
Fitting, socle	C₃×C₁₉²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉²

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1083

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22);(2,3)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)

1083 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2166, 21);