C₃⋊#595 #6077

order	204
isoclinism	isoclinic class of C₃⋊#595
automorphism	Aut(G) = D₃×AGL(1,𝔽₁₇) (order 1632) · Inn(G) = G · Out(G) = C₈
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇	C₄
prime radical, cosocle	C₃×D₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 51

A minimal faithful permutation representation — 2 generators on 20 points:

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

Polycyclic presentation:

2^2,3,17|a^2=b,c^a=c^2,d^a=d^4,d^b=d^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(204, 6);