C₄⋊Dic₁₇ #63226

order	272
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄⋊Dic₁₇

C₁₇ ⋊ C₄⋊C₄

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 2 generators on 25 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 13);