C₁₇×#13459 #16871203

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13459
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#13459

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#498
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#2058
prime radical	C₂³×C₁₇	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29,31,46)(21,34)(22,27)(23,39)(24,28)(25,32,41,48)(26,38)(30,43,33,45)(35,49)(36,40,47,44)(37,42);(20,30,31,33)(21,35)(25,40,41,44)(26,42)(29,45,46,43)(32,36,48,47)(34,49)(37,38);(18,20,23,30,24,31,22,33)(19,25,27,44,28,41,39,40)(21,36,38,32,35,47,37,48)(26,43,34,29,42,45,49,46)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6447);