C₁₃×#832 #11928104

order	1248
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₁₃ ⋊ #102
Sylow	C₃ ⋊ C₁₃×#102

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 216);