C₁₇×#13716 #16871460

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

Aliases

direct product

C₁₇×#13716

Subgroups

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

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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)(26,27,32,38)(28,33,42,55)(29,34,46,58)(30,47,49,76)(31,50,48,37)(35,59,61,43)(36,62,63,44)(39,51,68,79)(40,69,71,89)(41,72,70,54)(45,64,73,57)(52,80,82,65)(53,83,84,66)(56,75,60,74)(67,85,86,78)(77,88,81,87);(19,22)(23,25)(26,28,32,42)(27,33,38,55)(29,39,46,68)(30,40,49,71)(31,41,48,70)(34,51,58,79)(35,52,61,82)(36,53,63,84)(37,54,50,72)(43,65,59,80)(44,66,62,83)(45,67,73,86)(47,69,76,89)(56,77,60,81)(57,78,64,85)(74,87,75,88);(18,20,21,24)(19,23,22,25)(27,34)(29,43)(30,44)(31,48)(33,51)(35,36)(37,64)(38,58)(39,65)(40,66)(41,70)(45,75)(46,59)(47,56)(49,62)(50,57)(52,53)(54,85)(55,79)(60,76)(61,63)(67,88)(68,80)(69,77)(71,83)(72,78)(73,74)(81,89)(82,84)(86,87)

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, 6704);