C₃×#3622 #87965

order	408
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂³×AGL(1,𝔽₁₇) (order 2176) · Inn(G) = D₁₇ · Out(G) = C₂³×C₈
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₁₇ ⋊ C₃×C₈
Hall	C₃×C₁₇ ⋊ C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,22,24,19,21,25,20,23)(26,27,28);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 2);