C₁₇×#7480 #16865224

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7480

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#357
commutator	C₁₆	C₄²×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
socle	C₂×C₁₇	#1380
prime radical	C₂³×C₁₇	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

166 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 98 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)(18,19,22,28,25,32,46,31)(20,33,35,65,38,57,69,67)(21,39,42,63,44,62,80,29)(23,47,45,59,49,58,43,27)(24,50,41,30,48,60,79,61)(26,51,52,40,56,77,55,34)(36,71,70,64,73,54,78,81)(37,74,68,66,72,53,76,75);(18,20,23,36,48,72,44,34,46,69,43,78,41,68,42,77,25,38,49,73,24,37,21,40,22,35,45,70,79,76,80,51)(19,26,29,53,61,71,59,33,28,52,39,75,50,64,58,65,32,56,63,74,30,54,27,57,31,55,62,66,60,81,47,67)

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, 468);