C₁₇×#9983 #16867727

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9983

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₁₇×#2815	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

602 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 98 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)(19,24)(20,29)(21,33)(25,41)(26,30)(27,38)(28,40)(31,37)(32,48)(34,35)(39,43)(42,45)(44,47)(46,49);(18,19,23,28)(20,30,31,47)(21,25,35,43)(22,26,36,44)(24,37,40,29)(27,33,45,34)(32,39,48,41)(38,46,42,49);(19,25)(20,31)(21,34)(24,38)(26,27)(28,43)(29,37)(30,41)(32,49)(33,35)(39,47)(40,42)(44,45)(46,48)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2971);