C₁₃×#498 #11719033

order	832
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

98 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)(14,15,17,19)(16,20,21,18)(23,26)(24,28)(27,29);(14,16,17,21)(15,18,19,20);(22,23,24,26,25,27,28,29)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 999);