C₁₃×#819 #11928089

order	1248
isoclinism	isoclinic class of #204
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)(17,19,21,28,22,29,20,27)(18,23,24,26,25,31,30,32);(15,16)(17,18,20,24,22,25,21,30)(19,26,27,31,29,32,28,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 201);