C₁₇×#33983 #16891727

order	4352
nilpotency class	5
isoclinism	isoclinic class of #33982
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#33983

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	C₂²×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₁₇
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ #41×C₁₇ ◁ C₁₇×#131 ◁ C₁₇×#504 ◁ G

462 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 202 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 — 4 generators on 81 points:

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

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26971);