C₁₇×#10517 #16868261

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10517

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,28)(21,26)(22,25)(23,27)(24,30)(29,33)(31,32)(34,35,39,43)(36,44,47,59)(37,48,51,41)(38,52,54,42)(40,53,56,46)(45,61,49,60)(50,58,65,63)(55,62,57,64);(18,20)(19,24)(21,30)(22,31)(23,29)(25,33)(26,28)(27,32)(34,36,39,47)(35,40,43,56)(37,49,51,45)(38,53,54,46)(41,57,48,55)(42,59,52,44)(50,62,65,64)(58,60,63,61);(19,25)(20,29)(22,23)(26,27)(30,31)(32,33)(34,37,38,50,39,51,54,65)(35,41,42,58,43,48,52,63)(36,45,46,62,47,49,53,64)(40,55,44,60,56,57,59,61)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3505);