C₁₇×#13721 #16871465

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#13721

Subgroups

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

180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 2176

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

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6709);