C₁₇×#13362 #16871106

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13360
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13362

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#585	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

670 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,31,35,57)(21,36,41,61)(22,42,46,28)(23,47,24,29)(26,43,53,33)(27,40,56,39)(32,64,66,80)(34,69,48,63)(37,62,70,81)(38,73,44,71)(45,59,49,60)(50,74,79,72)(51,67,52,68)(54,65,78,77)(55,75,58,76);(18,20)(19,26)(21,37)(22,43)(23,34)(24,48)(25,35)(27,54)(28,57)(29,51)(30,53)(31,42)(32,40)(33,46)(36,50)(38,74)(39,66)(41,70)(44,72)(45,68)(47,52)(49,67)(55,64)(56,78)(58,80)(59,69)(60,63)(61,79)(62,73)(65,75)(71,81)(76,77);(18,21,25,41)(19,27,30,56)(20,32,35,66)(22,44,46,38)(23,40,24,39)(26,50,53,79)(28,58,42,55)(29,61,47,36)(31,62,57,81)(33,65,43,77)(34,70,48,37)(45,75,49,76)(51,54,52,78)(59,71,60,73)(63,80,69,64)(67,74,68,72)

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, 6350);