C₁₇×#7391 #16865135

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7389
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7391

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1333
commutator	C₁₆	C₂×C₈×C₁₇
Frattini, cosocle	#346	C₂²×C₁₇
prime radical	C₂²×C₁₇	#361
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₁₇×#346 ◁ G

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

normal subgroups only

This group has 116 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) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 81 points:

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

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 379);