C₁₉×ΓL(1,𝔽₈)×A₅ #37561653

order	23940
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×ΓL(1,𝔽₈)×A₅
unambiguous semidirect product	C₇⋊(C₃×C₁₉×A₅)
unambiguous semidirect product	(C₇×A₅)⋊(C₃×C₁₉)

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 665

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 785);