Q₈×D₁₇ #63255

order	272
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×D₁₇

Fitting	Q₈×C₁₇ ⋊ C₂
Sylow	C₁₇ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 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)(18,20,21,25)(19,22,23,24);(18,19,21,23)(20,24,25,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(272, 42);