C₃⋊#3622 #87966

order	408
isoclinism	isoclinic class of D₅₁
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅₁
commutator, hypocenter	C₃×C₁₇	C₈
Fitting, cosocle	C₃×C₄×C₁₇	C₂
socle, prime radical	C₂×C₃×C₁₇	C₄
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20)(21,22,23,25,24,26,27,28);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,20)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 3);