C₁₇×#12026 #16869770

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12026
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12026

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#427
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#1568
prime radical	C₂³×C₁₇	#108
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₁₇×#97 ◁ C₁₇×#405 ◁ G

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

normal subgroups only

This group has 180 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)(18,19,23,30,25,31,48,60,26,32,47,29,24,51,22,46)(20,33,36,53,38,62,35,54,39,58,49,75,37,71,69,27)(21,40,42,73,44,57,41,59,45,74,50,76,43,28,55,56)(34,63,65,52,67,77,79,72,68,81,70,78,66,61,64,80);(18,20,22,35,24,37,47,36,26,39,48,69,25,38,23,49)(19,27,29,33,31,53,46,62,32,54,30,58,51,75,60,71)(21,34,41,64,43,66,42,70,45,68,55,79,44,67,50,65)(28,52,56,61,40,72,73,63,57,78,59,77,74,80,76,81);(18,21,24,43,26,45,25,44)(19,28,31,40,32,57,51,74)(20,34,37,66,39,68,38,67)(22,41,47,42,48,55,23,50)(27,52,53,72,54,78,75,80)(29,56,46,73,30,59,60,76)(33,61,62,63,58,77,71,81)(35,64,36,70,69,79,49,65)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5014);