C₁₇×#13438 #16871182

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13438

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

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

normal subgroups only

This group has 406 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)(18,19,25,30)(20,31,36,56)(21,37,42,70)(22,43,24,28)(23,45,47,29)(26,35,51,33)(27,52,55,40)(32,61,64,81)(34,66,46,60)(38,71,62,77)(39,69,41,68)(44,57,48,59)(49,72,78,79)(50,65,58,67)(53,76,80,63)(54,73,75,74);(18,20,25,36)(19,26,30,51)(21,38,42,62)(22,35,24,33)(23,46,47,34)(27,53,55,80)(28,56,43,31)(29,58,45,50)(32,39,64,41)(37,61,70,81)(40,72,52,79)(44,65,48,67)(49,75,78,54)(57,60,59,66)(63,73,76,74)(68,77,69,71);(18,21,22,39,25,42,24,41)(19,27,28,54,30,55,43,75)(20,32,33,62,36,64,35,38)(23,40,44,73,47,52,48,74)(26,49,31,53,51,78,56,80)(29,37,57,68,45,70,59,69)(34,63,65,79,46,76,67,72)(50,77,60,61,58,71,66,81)

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, 6426);