order	136
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₇) (order 1088) · Inn(G) = D₁₇ · Out(G) = C₂²×C₈
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₁₇

Splittings

Fitting	C₄×C₁₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 68

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(136, 5);