C₁₇×#8798 #16866542

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#8798

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#382
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 2176

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)(18,19,23,27,24,28,22,32)(20,29,30,33,31,26,21,25)(34,35,39,45,40,43,38,44)(36,46,48,60,49,41,54,57)(37,50,52,59,53,61,55,42)(47,62,64,58,51,65,63,56);(18,20,22,21,24,31,23,30)(19,25,27,29,28,33,32,26)(34,36,38,48,40,49,39,54)(35,41,44,57,43,46,45,60)(37,51,52,64,53,47,55,63)(42,58,50,62,59,56,61,65);(18,21,22,31,24,30,23,20)(19,26,27,25,28,29,32,33)(34,37)(35,42,43,59)(36,47)(38,52)(39,55)(40,53)(41,56,46,58)(44,50,45,61)(48,63)(49,51)(54,64)(57,65,60,62)

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, 1786);