C₁₉×C₇⋊#1044 #27210900

order	13300
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₁₉×C₇⋊#1044
unambiguous semidirect product	C₇⋊(C₁₉×#1044)

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1330

A minimal faithful permutation representation — 2 generators on 36 points:

(2,3)(4,5)(6,7)(9,12,11,10)(14,17,16,15)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36);(1,2,4,6,7,5,3)(8,9,10,12,11)(13,14,17,15,16)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 58);