C₁₇×#7473 #16865217

order	4352
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7473

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	D₁₆
commutator	C₁₆	C₄²×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
socle	C₂²×C₁₇	#357
prime radical	C₂³×C₁₇	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

170 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 85
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 2 generators on 85 points:

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

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 461);