C₁₇×#13447 #16871191

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13447

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#2054
prime radical	C₁₇×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#405 ◁ G

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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)(20,33)(21,39)(22,46)(23,49)(24,29)(25,51)(26,32)(27,35)(28,42)(30,48)(31,47)(34,53)(36,63)(37,55)(38,62)(40,64)(41,72)(43,61)(44,75)(45,69)(50,57)(52,54)(56,68)(58,70)(59,73)(60,74)(65,77)(66,80)(67,79)(71,81)(76,78);(18,20)(19,27)(21,40)(22,36)(23,50)(24,35)(25,52)(26,38)(28,58)(29,54)(30,62)(31,63)(32,57)(33,46)(34,43)(37,47)(39,53)(41,66)(42,67)(44,65)(45,71)(48,68)(49,55)(51,56)(59,80)(60,81)(61,77)(64,72)(69,79)(70,73)(74,76)(75,78);(18,21,22,41,47,73,23,42,26,45,48,74,25,44,24,43)(19,28,29,59,51,72,30,39,32,61,49,75,31,60,46,69)(20,34,35,65,52,76,68,71,38,67,50,70,37,66,36,40)(27,53,33,64,63,80,55,58,57,79,62,81,56,78,54,77)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6435);