C₁₇×#13431 #16871175

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13429
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13431

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₂×#41×C₁₇	C₂³
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,29)(20,30,34,51)(21,35,39,53)(22,40,43,27)(23,28,45,54)(25,41,48,32)(26,44,50,38)(31,57,36,66)(33,56,62,80)(37,68,70,65)(42,64,71,52)(46,75,77,81)(47,73,78,60)(49,69,72,74)(55,61,79,59)(58,76,67,63);(18,20,24,34)(19,25,29,48)(21,36,39,31)(22,41,43,32)(23,33,45,62)(26,46,50,77)(27,51,40,30)(28,47,54,78)(35,63,53,76)(37,58,70,67)(38,59,44,61)(42,73,71,60)(49,79,72,55)(52,80,64,56)(57,68,66,65)(69,75,74,81);(18,21,22,37,24,39,43,70)(19,26,27,49,29,50,40,72)(20,31,32,58,34,36,41,67)(23,44,42,74,45,38,71,69)(25,46,30,55,48,77,51,79)(28,53,52,68,54,35,64,65)(33,61,60,75,62,59,73,81)(47,63,56,66,78,76,80,57)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6419);