C₁₃×#396 #11718931

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

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

186 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 897);