C₅×C₄⋊(C₃⋊C₁₆) #11746161

order	960
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₄⋊(C₃⋊C₁₆)
unambiguous semidirect product	C₄⋊(C₅×C₃⋊C₁₆)

Hall	C₃×C₅ ⋊ C₄⋊C₁₆
Sylow	C₃ ⋊ C₅×C₄⋊C₁₆

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 356);