C₁₃×#822 #11928093

order	1248
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₁₃ ⋊ #108
Sylow	C₃ ⋊ C₁₃×#108

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 2 generators on 32 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 205);