C₇×C₄⋊(C₃⋊C₁₆) #13051242

order	1344
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₄⋊(C₃⋊C₁₆)
unambiguous semidirect product	C₄⋊(C₇×C₃⋊C₁₆)

Hall	C₃×C₇ ⋊ C₄⋊C₁₆
Sylow	C₃ ⋊ C₇×C₄⋊C₁₆

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1344

A minimal faithful permutation representation — 2 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 531);