C₁₇×#7526 #16865270

order	4352
nilpotency class	6
isoclinism	isoclinic class of #7523
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7526

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1404
commutator	#125	C₂×C₄×C₁₇
Frattini, cosocle	#491	C₂²×C₁₇
prime radical	C₂²×C₁₇	AΣL(1,𝔽₁₆)
LCS	G ▷ #125 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#491 ◁ G

126 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 30 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 514);