C₁₇×#10217 #16867961

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10217

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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)(20,27)(21,23)(22,32)(24,26)(25,28)(29,33)(30,31)(34,35,40,45)(36,46,49,60)(37,50,53,58)(38,44,39,43)(41,54,56,48)(42,51,59,52)(47,55,63,57)(61,64,65,62);(18,20,23,29)(19,25,21,31)(22,30,24,28)(26,33,32,27)(34,36,40,49)(35,41,45,56)(37,47,53,63)(38,54,39,48)(42,57,59,55)(43,60,44,46)(50,61,58,65)(51,64,52,62);(18,21,23,19)(20,27,29,33)(22,32,24,26)(25,28,31,30)(34,37,40,53)(35,42,45,59)(36,47,49,63)(38,52,39,51)(41,55,56,57)(43,50,44,58)(46,61,60,65)(48,64,54,62)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3205);