C₁₇×#13702 #16871446

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13700
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#13702

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2215
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#2221	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#131 ◁ C₁₇×#504 ◁ G

184 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 70 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)(19,26)(20,33)(21,37)(22,24)(23,38)(27,41)(28,55)(29,49)(30,61)(31,47)(32,50)(34,65)(35,68)(36,42)(39,53)(40,54)(43,44)(45,56)(46,48)(51,60)(52,69)(57,76)(58,74)(59,73)(62,75)(63,66)(67,77)(71,79)(72,78)(80,81);(18,19,27,51,23,30,40,49,22,29,53,61,43,60,21,26,25,32,37,48,44,62,39,47,24,31,54,75,38,46,41,50)(20,28,52,76,35,57,63,55,42,59,65,79,70,80,34,45,36,58,66,72,68,78,69,74,33,56,77,81,64,71,67,73);(18,20)(19,28)(21,34)(22,42)(23,35)(24,33)(25,36)(26,45)(27,52)(29,59)(30,57)(31,56)(32,58)(37,66)(38,64)(39,69)(40,63)(41,67)(43,70)(44,68)(46,71)(47,74)(48,72)(49,55)(50,73)(51,76)(53,65)(54,77)(60,80)(61,79)(62,78)(75,81)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6690);