C₁₇×#8505 #16866249

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

Aliases

direct product

C₁₇×#8505

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#120
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#379
prime radical	C₁₇×#3531	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 648 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)(37,48,49,59)(38,43)(39,42)(41,50,56,52)(45,61)(46,58,51,55)(53,57)(54,63)(60,64)(62,65);(18,19)(20,24)(21,28)(22,25)(23,30)(26,31)(27,33)(29,32)(34,36)(35,40)(37,45)(38,51)(39,47)(41,54)(42,44)(43,58)(46,53)(48,61)(49,62)(50,64)(52,63)(55,57)(56,60)(59,65);(18,20,22,27)(19,24,25,33)(21,29,30,26)(23,31,28,32)(34,37)(35,41)(36,45)(38,52)(39,49)(40,54)(42,56)(43,59)(44,60)(46,64)(47,62)(48,57)(50,53)(51,63)(55,61)(58,65)

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, 1493);