C₁₇×#10211 #16867955

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 406 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)(18,19,26,32)(20,33,39,47)(21,40,44,35)(22,45,50,68)(23,51,56,64)(24,34,58,70)(25,31,54,67)(27,59,37,41)(28,61,65,49)(29,55,69,81)(30,48,71,74)(36,72,63,80)(38,62,73,79)(42,78,57,52)(43,76,77,46)(53,75,66,60);(18,20,25,38)(19,21,31,43)(22,46,49,35)(23,52,55,36)(24,27,48,60)(26,39,54,73)(28,62,45,33)(29,66,64,41)(30,57,70,80)(32,44,67,77)(34,72,71,42)(37,74,75,58)(40,50,76,61)(47,65,79,68)(51,59,69,53)(56,78,81,63);(18,21,25,43)(19,27,31,60)(20,34,38,71)(22,47,49,79)(23,53,55,59)(24,57,48,80)(26,44,54,77)(28,63,45,78)(29,46,64,35)(30,39,70,73)(32,37,67,75)(33,61,62,50)(36,68,52,65)(40,69,76,51)(41,56,66,81)(42,74,72,58)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3199);