C₁₇×#13708 #16871452

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#13708

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

158 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 89
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 89 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(26,27,29,33)(28,38,39,67)(30,46,43,68)(31,51,44,76)(32,53,45,37)(34,58,55,40)(35,61,56,49)(36,64,57,48)(41,72,70,89)(42,73,54,69)(47,65,74,87)(50,83,75,79)(52,62,77,86)(59,84,85,81)(60,71,66,80)(63,82,78,88);(18,20,21,25)(19,22,23,24)(27,33)(34,55)(35,56)(36,57)(37,53)(38,67)(46,68)(51,76)(59,85)(60,66)(62,86)(63,78)(65,87)(69,73)(72,89)(79,83);(26,28,29,39)(27,34,33,55)(30,47,43,74)(31,52,44,77)(32,54,45,42)(35,62,56,86)(36,65,57,87)(37,66,53,60)(38,68,67,46)(40,61,58,49)(41,64,70,48)(50,84,75,81)(51,59,76,85)(63,89,78,72)(69,79,73,83)(71,82,80,88)

Conjugacy classes & character table

833 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6696);