C₁₇×#8476 #16866220

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#8476

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#3512	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 678 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) = 2176

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1464);