C₇×#4504 #13051286

order	1344
isoclinism	isoclinic class of D₄₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #366
Sylow	C₃ ⋊ C₇×#366

92 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)(15,16,21,27,18,22,25,28,19,23,29,30,24,26,17,20);(9,10)(11,12,13,14)(16,20)(17,21)(18,24)(22,30)(23,28)(25,29)(26,27)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 575);