C₁₇×#9502 #16867246

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×#9502

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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)(20,24,29,37)(21,31,33,25)(22,26)(23,27)(28,36,42,48)(30,38,41,47)(32,35)(34,39,46,40)(43,45,44,49);(18,20,23,30)(19,24,35,47)(21,28,33,43)(22,29,32,41)(25,36,39,48)(26,37,27,38)(31,45,40,49)(34,44,46,42);(18,21,32,46)(19,25,35,39)(20,28,41,42)(22,34,23,33)(24,36,47,48)(26,40,27,31)(29,44,30,43)(37,49,38,45)

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, 2490);