C₁₇×#8527 #16866271

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#8527

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 656 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)(18,19,22,27,23,26,21,25)(20,28,29,33,30,24,31,32)(34,35)(36,44,47,56)(37,48,50,41)(38,42)(39,43)(40,46,54,51)(45,59)(49,63,65,55)(52,57)(53,60)(58,61)(62,64);(18,20,23,30)(19,24,26,28)(21,29,22,31)(25,32,27,33)(34,36)(35,40)(37,45)(38,51)(39,47)(41,53)(42,56)(43,54)(44,57)(46,52)(48,62)(49,64)(50,61)(55,59)(58,63)(60,65);(18,21,23,22)(19,25,26,27)(20,29,30,31)(24,32,28,33)(34,37,39,50)(35,41,43,48)(36,45,47,61)(38,49,52,65)(40,53,54,62)(42,55,57,63)(44,58,56,59)(46,60,51,64)

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, 1515);