C₁₇×#10210 #16867954

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10210

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 440 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)(20,27)(21,22)(24,28)(25,31)(29,30)(32,33)(34,35)(36,46)(37,51)(38,44)(39,43)(40,45)(41,48)(42,52)(47,58)(49,57)(50,56)(53,60)(54,59)(55,63)(61,62)(64,65);(18,19)(20,28)(21,25)(22,31)(23,26)(24,30)(27,32)(29,33)(34,36,40,50)(35,41,45,57)(37,47,53,63)(38,49,39,48)(42,58,59,55)(43,56,44,46)(51,61,60,65)(52,64,54,62);(18,20)(19,24)(21,30)(22,27)(23,29)(25,33)(26,32)(28,31)(34,37,40,53)(35,42,45,59)(36,47,50,63)(38,52,39,54)(41,55,57,58)(43,51,44,60)(46,61,56,65)(48,62,49,64)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3198);