Dic₆₆ #63155

order	264
isoclinism	isoclinic class of Dic₆₆
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

Dic₆₆

	subgroup	G/H
center, Frattini	C₂	C₂×D₃₃
commutator, socle, prime radical, cosocle	C₂×C₃×C₁₁	C₂²
Fitting	C₃×C₄×C₁₁	C₂
hypercenter	C₄	D₃₃
hypocenter	C₃×C₁₁	Q₈
LCS	G ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3,4)(5,8,7,6)(9,10,11)(12,13,14,15,16,17,18,19,20,21,22);(1,5,3,7)(2,6,4,8)(10,11)(13,22)(14,21)(15,20)(16,19)(17,18)

Polycyclic presentation:

2^3,3,11|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 23);