D₁₃₆ #63220

order	272
isoclinism	isoclinic class of #63219
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₁₃₆

Fitting	C₈×C₁₇ ⋊ C₂
Sylow	C₁₇ ⋊ D₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 136

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

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 7);