C₁₇×#7421 #16865165

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7421

Subgroups

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

140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 89 points:

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

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, 409);