C₂₉×#461 #14270756

order	1856
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₂₉
prime radical	C₂×D₄×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 3 generators on 41 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)(31,33)(34,35,37,40)(36,38,41,39);(30,31,32,33);(35,38)(36,41)(39,40)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1856, 142);