C₂₉×C₄⋊Dic₃ #13063547

order	1392
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₉×C₄⋊Dic₃
unambiguous semidirect product	C₄⋊(Dic₃×C₂₉)

Hall	C₃×C₂₉ ⋊ C₄⋊C₄
Sylow	C₃ ⋊ C₄⋊C₄×C₂₉

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1392

A minimal faithful permutation representation — 2 generators on 40 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 58);