C₁₇×#9985 #16867729

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9985

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 502 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)(20,23)(21,24)(22,25)(26,29)(27,30)(28,32)(31,33)(34,35,40,45)(36,46,49,57)(37,42,53,60)(38,44,39,43)(41,50,56,48)(47,62,63,58)(51,65,64,55)(52,61,54,59);(18,20,22,27)(19,23,25,30)(21,26,28,33)(24,31,32,29)(34,36)(35,41)(37,51)(38,50)(39,48)(40,49)(42,58)(43,57)(44,46)(45,56)(47,52)(53,64)(54,63)(55,59)(60,62)(61,65);(18,21)(19,24)(20,26)(22,28)(23,29)(25,32)(27,33)(30,31)(34,37,40,53)(35,42,45,60)(36,47,49,63)(38,52,39,54)(41,55,56,65)(43,59,44,61)(46,58,57,62)(48,51,50,64)

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, 2973);