C₁₇×#7207 #16864951

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7207

Subgroups

	subgroup	G/H
center	C₈×C₁₇	#99
commutator	C₂³	C₄×C₈×C₁₇
Frattini, cosocle	C₂×#131	C₂²×C₁₇
socle	C₂×C₁₇	#1282
prime radical	C₂×#41×C₁₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

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

normal subgroups only

This group has 248 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 — 2 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,31,44,55,25,30,23,29,43,54,45,56)(20,32,34,57,36,60,65,79,37,59,35,58,64,78,66,80)(21,38,39,53,40,67,68,77,41,27,42,50,69,51,70,75)(26,46,47,71,49,72,73,33,48,61,52,62,74,81,76,63);(18,20,23,35,24,36,45,66,25,37,22,34,43,64,44,65)(19,26,29,47,31,49,56,73,30,48,28,52,54,74,55,76)(21,33,39,61,40,62,68,81,41,63,42,46,69,71,70,72)(27,32,50,58,51,60,75,80,38,59,53,57,67,78,77,79)

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, 195);