C₁₇×#8544 #16866288

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#8544

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂³×D₄×C₁₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

1222 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 41
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1532);