C₁₇×#11914 #16869658

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11914

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1530
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	#97	C₂³×C₁₇
prime radical	C₂³×C₁₇	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#405 ◁ G

272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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 — 3 generators on 81 points:

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

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, 4902);