C₂₉×SL(2,ℤ/4) #13063587

order	1392
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₉×SL(2,ℤ/4)
unambiguous semidirect product	A₄⋊(C₄×C₂₉)

A₄ ⋊ C₄×C₂₉

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 348

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33)(34,35,37,36);(35,36,37)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 98);