C₁₇×#33982 #16891726

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

Aliases

direct product

C₁₇×#33982

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

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

normal subgroups only

This group has 472 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)(20,26)(21,25)(22,39)(23,42)(24,30)(27,35)(28,36)(29,40)(31,47)(32,43)(33,61)(34,62)(37,54)(38,46)(41,68)(44,64)(45,63)(48,58)(49,59)(50,57)(51,67)(52,65)(53,66)(55,69)(56,79)(60,75)(70,80)(71,78)(72,76)(73,77)(74,81);(19,25)(21,35)(22,36)(23,40)(26,43)(27,28)(29,54)(30,46)(32,58)(33,59)(34,57)(37,67)(38,65)(39,44)(41,66)(42,45)(47,69)(48,49)(50,75)(51,68)(52,53)(55,76)(56,77)(60,81)(61,70)(62,71)(63,64)(72,73)(74,79)(78,80);(18,20)(19,26)(21,32)(22,33)(23,34)(24,31)(25,43)(27,48)(28,49)(29,50)(30,47)(35,58)(36,59)(37,60)(38,55)(39,61)(40,57)(41,56)(42,62)(44,70)(45,71)(46,69)(51,74)(52,72)(53,73)(54,75)(63,78)(64,80)(65,76)(66,77)(67,81)(68,79);(20,31)(26,47)(32,55)(33,56)(34,57)(43,69)(48,72)(49,73)(50,62)(58,76)(59,77)(60,78)(61,79)(70,74)(71,75)(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, 26970);