C₂₃×#681 #14270271

order	1840
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₅×C₂₃ ⋊ M₁₆
Sylow	C₅ ⋊ M₁₆×C₂₃

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 920

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1840, 54);