C₃⋊#3624 #87969

order	408
isoclinism	isoclinic class of C₃⋊#595
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#595
commutator, hypocenter	C₃×C₁₇	C₈
Fitting, socle, prime radical	C₂×C₃×C₁₇	C₄
cosocle	C₃×Dic₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂

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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 6);