C₁₇×#10669 #16868413

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10669

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#399
prime radical	C₂³×C₁₇	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 296 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) = 65
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 65 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3657);