D₃×C₄₇ #63337

order	282
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×D₃×C₂₃ (order 276) · Inn(G) = D₃ · Out(G) = C₂×C₂₃
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₄₇
unambiguous semidirect product	C₃⋊(C₂×C₄₇)

Fitting, socle, Hall	C₃×C₄₇ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄₇

	subgroup	G/H
center, hypercenter	C₄₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₃×C₄₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₄₇

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 141

A minimal faithful permutation representation — 2 generators on 50 points:

(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);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(282, 1);