C₂₉×#466 #14270761

order	1856
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

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

134 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)(30,31)(32,33)(35,38)(36,39)(40,41);(34,35,39,41,37,40,36,38);(31,33)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1856, 147);