C₇×#4461 #13051241

order	1344
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₈ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #346
Sylow	C₃ ⋊ C₇×#346

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1344

A minimal faithful permutation representation — 2 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 530);