C₈×D₁₇ #63217

order	272
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂³×AGL(1,𝔽₁₇) (order 2176) · Inn(G) = D₁₇ · Out(G) = C₂³×C₈
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₈×D₁₇

Fitting	C₈×C₁₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₈

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:

(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)(18,19,20,22,21,23,24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 4);