C₃×#89421 #13055083

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

Hall	C₃×C₇ ⋊ C₄×C₄⋊C₄
Sylow	C₇ ⋊ C₃×C₄×C₄⋊C₄

388 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1344

A minimal faithful permutation representation — 3 generators on 22 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4372);