C₃×C₄⋊#672 #11746039

order	960
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊#672
unambiguous semidirect product	C₄⋊(C₃×#672)

Hall	C₃×C₅ ⋊ C₄⋊C₁₆
Sylow	C₅ ⋊ C₃×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)(4,5,7,8,6)(9,10,11,12);(5,6)(7,8)(10,12)(13,14,15,18,16,19,21,24,17,20,22,25,23,26,27,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 234);