C₁₇×#9512 #16867256

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#9512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
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

558 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 118 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)(18,19,23,28,22,20,25,31)(21,26,33,42,32,29,37,44)(24,27,38,39,35,30,40,36)(34,43,47,48,45,41,49,46);(18,20,23,36,22,19,25,39)(21,29,37,48,32,26,33,46)(24,30,38,31,35,27,40,28)(34,41,49,42,45,43,47,44);(18,21,24,34)(19,26,27,43)(20,29,30,41)(22,32,35,45)(23,37,38,49)(25,33,40,47)(28,44,39,46)(31,42,36,48)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2500);