C₁₃×#397 #11718932

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

170 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 416

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)(24,28)(25,26)(27,29);(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, 898);