C₁₇×#8495 #16866239

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#8495

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

620 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 142 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)(19,23,25,28)(24,32,33,31)(34,35)(36,44,47,40)(37,48,50,57)(38,43)(39,42)(41,49,55,51)(45,60)(46,59,64,54)(52,56)(53,61)(58,63)(62,65);(18,19)(20,24)(21,28)(22,25)(23,30)(26,31)(27,33)(29,32)(34,36,39,47)(35,40,42,44)(37,45,50,62)(38,46,52,64)(41,53,55,58)(43,54,56,59)(48,65,57,60)(49,61,51,63);(18,20,22,27)(19,24,25,33)(21,29,30,26)(23,31,28,32)(34,37)(35,41)(36,45)(38,51)(39,50)(40,53)(42,55)(43,57)(44,58)(46,63)(47,62)(48,56)(49,52)(54,60)(59,65)(61,64)

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, 1483);