C₁₇×#8791 #16866535

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8790
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#8791

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#382
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 65
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,24)(22,32)(23,27)(25,30)(26,29)(31,33)(34,35)(36,44,48,40)(37,49,51,64)(38,43)(39,42)(41,50,55,59)(45,52)(46,60)(47,57,58,54)(53,61)(56,65)(62,63);(18,20,29,31,23,30,22,21)(19,24,32,25,27,33,26,28)(34,36,45,58,39,48,38,47)(35,40,52,57,42,44,43,54)(37,46,59,65,51,62,50,61)(41,53,64,60,55,56,49,63);(18,21,22,30,23,31,29,20)(19,25,26,24,27,28,32,33)(34,37)(35,41,42,55)(36,46)(38,50)(39,51)(40,53,44,56)(43,49,52,64)(45,59)(47,61)(48,62)(54,63,57,60)(58,65)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1779);