C₁₃×C₁₃⋊C₃×A₅ #44478357

order	30420
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₁₃⋊C₃×A₅
unambiguous semidirect product	C₁₃⋊(C₃×C₁₃×A₅)
unambiguous semidirect product	(C₁₃×A₅)⋊(C₃×C₁₃)

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 195

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3)(6,16,10)(7,9,8)(11,17,12)(14,18,15);(1,5,4)(6,7,8)(9,11,14)(10,13,17)(12,16,15)(19,20,21,22,23,24,25,26,27,28,29,30,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 946);