C₁₃×#944 #11928917

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₁₃ ⋊ C₄⋊Q₈
Sylow	C₃ ⋊ C₁₃×C₄⋊Q₈

136 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1248

A minimal faithful permutation representation — 3 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1029);