Dic₃×D₁₃ #64599

order	312
isoclinism	isoclinic class of D₃×D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₃×D₁₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃	C₂²
prime radical	C₂×C₃×D₁₃	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 20 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16);(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,16)(17,18,19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 15);