C₁₇×#8521 #16866265

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#8521

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 690 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)(20,26,28,23)(21,24)(22,25)(27,32,33,30)(29,31)(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)(19,23)(21,27)(22,28)(24,30)(25,26)(29,33)(31,32)(34,36,39,47)(35,40,43,54)(37,45,50,61)(38,51,52,46)(41,53,48,62)(42,56,57,44)(49,64,65,60)(55,59,63,58);(18,21,22,29)(19,24,25,31)(20,27,28,33)(23,30,26,32)(34,37)(35,41)(36,45)(38,49)(39,50)(40,53)(42,55)(43,48)(44,58)(46,60)(47,61)(51,64)(52,65)(54,62)(56,59)(57,63)

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, 1509);