C₁₃×#398 #11718933

order	832
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

150 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 899);