C₁₇×#8799 #16866543

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×#8799

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

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, 1787);