C₃⋊Dic₃₉ #90852

order	468
isoclinism	isoclinic class of C₃⋊D₃₉
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

C₃⋊Dic₃₉

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₃₉
commutator, hypocenter	C₃²×C₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₁₃	C₂
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 468

A minimal faithful permutation representation — 3 generators on 23 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,17)(19,20)(22,23);(1,2,4,6,8,10,12,13,11,9,7,5,3)(21,22,23);(18,19,20)

Polycyclic presentation:

2^2,3^2,13|a^2=b,c^a=c^2,d^a=d^2,e^a=e^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 27);