C₇×C₃⋊(C₁₁⋊C₈) #14270426

order	1848
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₃⋊(C₁₁⋊C₈)
unambiguous semidirect product	C₃⋊(C₇×C₁₁⋊C₈)
unambiguous semidirect product	C₁₁⋊(C₇×C₃⋊C₈)

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1848

A minimal faithful permutation representation — 2 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1848, 9);