C₃×C₂²⋊C₄×C₂₉ #13063571

order	1392
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

C₃×C₂²⋊C₄×C₂₉

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 696

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(4,5,7,9)(6,8,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(5,8)(9,11)

maximal subgroup of	C₃×C₄×D₄×C₂₉
maximal normal subgroup of	C₃×C₄×D₄×C₂₉

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 82);