C₁₇×#13709 #16871453

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13709
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#13709

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2226
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#508	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 154 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)(18,19,25,31)(20,30,35,62)(21,36)(22,41,43,28)(23,44,47,70)(24,48,33,26)(27,52)(29,58,60,46)(32,63)(34,67,69,57)(37,74)(38,56)(39,71)(40,75)(42,51,78,79)(45,61)(49,73)(50,77)(53,76)(54,80)(55,68)(59,64)(65,72)(66,81);(18,20,22,33,25,35,43,24)(19,26,28,30,31,48,41,62)(21,32,37,64,40,66,39,49)(23,34,42,58,47,69,78,46)(27,50,53,61,56,54,55,72)(29,51,57,44,60,79,67,70)(36,59,71,63,75,73,74,81)(38,65,76,80,52,45,68,77);(18,21)(19,27)(20,32)(22,37)(23,45)(24,49)(25,40)(26,50)(28,53)(29,59)(30,61)(31,56)(33,64)(34,68)(35,66)(36,70)(38,58)(39,43)(41,55)(42,77)(44,75)(46,52)(47,65)(48,54)(51,71)(57,63)(60,73)(62,72)(67,81)(69,76)(74,79)(78,80)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6697);