C₁₇×#13075 #16870819

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13075

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂×#41×C₁₇	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

458 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 146 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)(20,30)(21,36,38,26)(22,40)(23,45)(24,28)(25,33)(27,43)(29,42)(31,53)(32,54,61,74)(34,57)(35,67)(37,70,41,72)(39,51,71,69)(44,46)(47,60,68,63)(48,58)(49,65)(50,59,52,73)(55,66)(56,64)(62,80,79,76)(75,81,77,78);(18,20,31,58,23,35,22,33,24,34,43,66,42,64,44,65)(19,25,46,67,29,48,27,30,28,49,40,56,45,55,53,57)(21,32,59,78,39,62,41,63,38,61,73,81,71,79,37,60)(26,47,72,80,51,75,52,54,36,68,70,76,69,77,50,74);(18,21)(19,26)(20,32)(22,41)(23,39)(24,38)(25,47)(27,52)(28,36)(29,51)(30,54)(31,59)(33,63)(34,61)(35,62)(37,44)(40,70)(42,71)(43,73)(45,69)(46,72)(48,75)(49,68)(50,53)(55,77)(56,76)(57,74)(58,78)(60,65)(64,79)(66,81)(67,80)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6063);