C₁₇×#13441 #16871185

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13441

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#405 ◁ G

378 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 85
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 85 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,28,33)(24,34,38,66)(25,39,44,57)(26,45,49,64)(27,50,47,32)(29,52,55,36)(30,41,59,42)(31,60,62,48)(35,67,70,83)(37,71,51,61)(40,65,68,56)(43,79,76,73)(46,63,81,54)(53,74,82,69)(58,78,72,77)(75,84,80,85);(22,24,28,38)(23,29,33,55)(25,40,44,68)(26,46,49,81)(27,51,47,37)(30,56,59,65)(31,61,62,71)(32,63,50,54)(34,64,66,45)(35,41,70,42)(36,60,52,48)(39,53,57,82)(43,80,76,75)(58,85,72,84)(67,73,83,79)(69,78,74,77);(19,21)(22,25,26,41,47,76,60,78,28,44,49,42,27,43,48,77)(23,30,31,57,50,72,64,73,33,59,62,39,32,58,45,79)(24,35,36,68,51,74,81,75,38,70,52,40,37,69,46,80)(29,53,34,65,63,83,71,84,55,82,66,56,54,67,61,85)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6429);