C₁₃×#468 #11719003

order	832
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₃
prime radical	C₁₃×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

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)(14,15)(16,17)(19,22)(20,24)(23,25);(18,19,20,22,21,23,24,25);(15,17)(19,23)(22,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 969);