C₂²×D₃₉ #64644

order	312
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×D₃₉

	subgroup	G/H
center, hypercenter	C₂²	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂²

64 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 60);