C₃⋊(D₁₉⋊C₃) #66793

order	342
isoclinism	isoclinic class of C₃⋊(D₁₉⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(D₁₉⋊C₃)
unambiguous semidirect product	(C₁₉⋊C₃)⋊D₃
unambiguous semidirect product	D₅₇⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 57

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

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

Polycyclic presentation:

2,3^2,19|c^a=c^2,d^a=d^18,d^b=d^7

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(342, 11);