C₁₇×#7479 #16865223

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

Aliases

direct product

C₁₇×#7479

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	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 162 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)(18,19,22,28,25,32,45,31)(20,33,35,65,38,56,70,66)(21,39,42,62,43,29,46,60)(23,27,44,57,47,59,78,58)(24,48,41,30,49,61,77,63)(26,50,51,40,55,76,54,34)(36,71,69,81,68,64,79,53)(37,72,67,52,73,80,75,74);(18,20,23,36,24,37,46,50,45,70,78,79,77,75,43,34,25,38,47,68,49,73,42,76,22,35,44,69,41,67,21,40)(19,26,29,52,30,53,58,65,28,51,60,80,61,71,27,56,32,55,39,74,63,81,57,66,31,54,62,72,48,64,59,33)

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, 467);