C₁₃×#450 #11718985

order	832
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

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

188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 208

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 951);