C₁₇×#8759 #16866503

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#8759

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#381
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

474 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,29,24,28,20,30)(21,34,32,48,36,43,37,40)(23,27,38,41,31,39,33,25)(26,42,44,35,45,49,46,47);(18,20,31,38)(19,25,39,29)(21,32,47,42)(22,23,33,24)(26,40,34,46)(27,30,28,41)(35,49,36,37)(43,44,45,48);(18,21)(19,26,27,43)(20,32)(22,37)(23,35)(24,36)(25,40,30,44)(28,45,39,34)(29,46,41,48)(31,47)(33,49)(38,42)

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, 1747);