C₁₇×#10566 #16868310

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10564
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10566

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#394
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

490 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 1088

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)(20,22)(21,23)(24,25)(26,27,31,35)(28,33,37,41)(29,38,36,32)(30,40,39,34);(18,20)(19,22)(21,24)(23,25)(26,28,31,37)(27,32,35,38)(29,39,36,30)(33,34,41,40);(22,25)(26,29,30,28,31,36,39,37)(27,33,34,38,35,41,40,32)

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, 3554);