Dic₃×D₂₁ #92685

order	504
isoclinism	isoclinic class of D₃×D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₃×D₂₁

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₂₁
commutator, hypocenter	C₃²×C₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₇	C₂²
prime radical	C₂×C₃×D₂₁	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 17 points:

(1,2,3)(5,6)(12,13)(14,15)(16,17);(2,3)(4,5,6)(7,8,9,10)(11,12,14,16,17,15,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 111);