Dic₃×C₁₇² #16812397

order	3468
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇² · Schur multiplier (H₂) = C₁₇

Aliases

direct product	Dic₃×C₁₇²
unambiguous semidirect product	C₃⋊(C₄×C₁₇²)

derived, Sylow	C₃ ⋊ C₄×C₁₇²
Hall	C₃×C₁₇² ⋊ C₄

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 3468

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24);(1,3,2,4)(6,7)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)

1734 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3468, 19);