D₃×C₄₃ #63108

order	258
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×C₃×D₃×C₇ (order 252) · Inn(G) = D₃ · Out(G) = C₂×C₃×C₇
homology	Abelianization (H₁) = C₂×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₄₃
unambiguous semidirect product	C₃⋊(C₂×C₄₃)

Fitting, socle, Hall	C₃×C₄₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄₃

	subgroup	G/H
center, hypercenter	C₄₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₄₃

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 129

A minimal faithful permutation representation — 2 generators on 46 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);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(258, 3);