C₃⋊Dic₃₃ #87683

order	396
isoclinism	isoclinic class of C₃⋊D₃₃
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊Dic₃₃
unambiguous semidirect product	C₁₁⋊(C₃⋊Dic₃)

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₃₃
commutator, hypocenter	C₃²×C₁₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₁₁	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 396

A minimal faithful permutation representation — 3 generators on 21 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 15);