C₂×Dic₃×C₁₇ #87986

order	408
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×Dic₃×C₁₇
unambiguous semidirect product	(C₂×C₃)⋊(C₄×C₁₇)

derived, Sylow	C₃ ⋊ C₂×C₄×C₁₇
Hall	C₃×C₁₇ ⋊ C₂×C₄

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 408

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 23);