C₁₇×#12437 #16870181

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12437

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

214 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 74 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)(18,19,26,33)(20,34,40,64)(21,41,44,72)(22,30,46,58)(23,29,45,59)(24,32,25,31)(27,49,54,36)(28,55,57,42)(35,65,68,76)(37,53,69,52)(38,63,39,51)(43,73,48,60)(47,61,74,56)(50,67,77,71)(62,75,79,66)(70,80,81,78);(18,20,23,37,24,38,46,49,26,40,45,69,25,39,22,36)(19,27,30,51,31,52,59,64,33,54,58,63,32,53,29,34)(21,35,47,70,43,67,55,75,44,68,74,81,48,71,42,66)(28,50,60,78,56,76,72,79,57,77,73,80,61,65,41,62);(18,21)(19,28)(20,35)(22,42)(23,47)(24,43)(25,48)(26,44)(27,50)(29,41)(30,60)(31,56)(32,61)(33,57)(34,62)(36,66)(37,70)(38,67)(39,71)(40,68)(45,74)(46,55)(49,75)(51,78)(52,76)(53,65)(54,77)(58,73)(59,72)(63,80)(64,79)(69,81)

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, 5425);