C₁₃×C₄⋊Dic₅ #11760132

order	1040
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₄⋊Dic₅
unambiguous semidirect product	C₄⋊(C₁₃×Dic₅)

Hall	C₅×C₁₃ ⋊ C₄⋊C₄
Sylow	C₅ ⋊ C₁₃×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1040

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1040, 61);