C₁₉×#926 #14269678

order	1824
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₁₉ ⋊ #117
Sylow	C₃ ⋊ C₁₉×#117

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 912

A minimal faithful permutation representation — 3 generators on 34 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 905);