Dic₃×Dic₇ #66572

order	336
isoclinism	isoclinic class of D₃×D₇
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×D₇
commutator, hypocenter	C₃×C₇	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₇	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂²

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 18 points:

(2,3)(4,5)(6,7)(8,9,10)(15,16,17,18);(1,2,4,6,7,5,3)(9,10)(11,12,13,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 41);