C₁₇×#9334 #16867078

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9331
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9334

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

398 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,22,26,23,25,32,20)(21,28,30,33,29,24,31,27)(34,35,39,43,40,45,38,44)(36,46,49,56,50,59,48,41)(37,51,53,42,54,57,52,58)(47,55,62,64,63,65,61,60);(18,20,22,25,23,26,32,19)(21,27,31,28,29,33,30,24)(34,36)(35,41,45,56)(37,47)(38,48)(39,49)(40,50)(42,55,58,65)(43,46,44,59)(51,60,57,64)(52,61)(53,62)(54,63);(18,21,23,29)(19,24,25,28)(20,27,26,33)(22,31,32,30)(34,37,40,54)(35,42,45,58)(36,47,50,63)(38,53,39,52)(41,55,56,65)(43,51,44,57)(46,60,59,64)(48,62,49,61)

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, 2322);