C₁₇×#8783 #16866527

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8603
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#8783

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#117
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#382
prime radical	C₂³×C₁₇	#117
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#376 ◁ G

262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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)(18,19,22,25,21,24,29,32)(20,26,28,33,27,23,30,31)(34,35)(36,44,47,40)(37,48,50,63)(38,43)(39,42)(41,49,54,64)(45,58)(46,57,61,53)(51,55)(52,59)(56,65)(60,62);(18,20)(19,23)(21,27)(22,28)(24,26)(25,31)(29,30)(32,33)(34,36,38,46,39,47,51,61)(35,40,43,53,42,44,55,57)(37,45,49,59,50,60,64,65)(41,52,48,62,54,56,63,58);(20,27)(23,26)(28,30)(31,33)(34,37)(35,41,42,54)(36,45)(38,49)(39,50)(40,52,44,56)(43,48,55,63)(46,59)(47,60)(51,64)(53,62,57,58)(61,65)

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, 1771);