C₁₃×C₃⋊SL(2,ℤ/4) #14273102

order	1872
isoclinism	isoclinic class of C₃⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₁₃×C₃⋊SL(2,ℤ/4)
unambiguous semidirect product	C₃⋊(C₁₃×SL(2,ℤ/4))
unambiguous semidirect product	A₄⋊(Dic₃×C₁₃)

C₃×A₄ ⋊ C₄×C₁₃

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 468

A minimal faithful permutation representation — 3 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1872, 730);